TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning
Authors: Andreas Auer
Patrick Podest
Daniel Klotz
Sebastian Böck
Günter Klambauer
Sepp Hochreiter
Venue: NeurIPS 2025 poster ()
Keywords: xLSTM
Time Series Forecasting
Zero-Shot Forecasting
Pre-Trained Models
Primary area: deep_learning

Abstract: In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. 
This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, 
making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce.
Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series forecasting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities, they lack strong in-context learning abilities.
We introduce *TiRex* that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or parallelizable RNNs such as RWKV, TiRex retains state tracking, a critical property for long-horizon forecasting. To further facilitate its state-tracking ability, we propose a training-time masking strategy called CPM.
TiRex sets a new state of the art in zero-shot time series forecasting on the Hugging Face benchmarks *GiftEval* and *Chronos-ZS*, outperforming significantly larger models including *TabPFN-TS* (Prior Labs), *Chronos Bolt* (Amazon), *TimesFM* (Google), and *Moirai* (Salesforce) across both short- and long-term forecasts.

TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning
Andreas Auer 1,2 Sebastian Böck
Patrick Podest
Daniel Klotz Sepp Hochreiter 1.2
Günter Klambauer
NXAI GmbH, Linz, Austria
ELLIS Unit, LIT AI Lab, Institute for Machine Learning, JKU Linz, Austria 3 Interdiscipllnnry Transformation University Austria, Linz, Austria
Abstract
In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce. Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series fore- casting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities. they lack strong in-context learning abilities. We introduce TiRex that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or paralleliz- able RNNs such as RWKV, TiRex retains state-tracking, a critical property for long-horizon forecasting. To further facilitate its trac-ing ability, we propose a training- time masking strategy called CPM. TiRex sets new state of the art in zero-shot time series forecasting on the HuggingTace benchmarks GiftEval and Chronos-ZS, outperforming significantly larger models including TabPFN-TS (Prior Labs), Chronos Boli (Amazon), TimesFM (Google), and Moirai (Salesforce) across both short- and long-ten term forecasts.
1 Introduction
Recent research in time series forecasting has adopted in-context learning through large-scale pre- trained models, analogous large language models (Woo et al. 2024 Ansari al. 2024a Das et al. 2024). These models enable zero-shot forecasting, allowing them to generalize to unseen datasets without parameter updates, akin meta-learning! (Hccreiter al. (2001). This capability empowers practitioners without machine learning expertise to use advanced forecasting tools. More importantly, zero-shot forecasting significantly improves performance in data-scarce settings, where training task-specific models often fail to generalize. As a result, in-context learning models hold promise for broad adoption in domains such energy, retail, or healthcare.
Most pre-trained time series models are based on transformer architectures (Vaswani et al. 2017). which are well suited for in-context learning, but despite their success in language, often fall short of expectations in time series forecasting (e.g., Zeng et al. 2023). In contrast, LSTMs (Hochreiter) 1991 Hochreiter & Schmidhuber 1997) have demonstrated strong results in time series forecasting due to their recurrence and effective state-tres trattettaciing (e.g., Nearing et al.) 2024). Therefore, LSTMs are more
expressive than state-space models (SSMs), parallelizable RNNs like RWKV (Peng al. 2023) and
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Two exemplary time series from the GvftEval benchmark. For both examples, we show one plot with the full context and TiRex's prediction, well as zoomed-in forecasts of the best- performing zero-shot models. Each plot shows the ground truth signal in blue, the model's (median) prediction in orange, and the uncertainty bounds in gray. (a) A time series that exhibits strong peaks. Only TiRex is capable of predicting the periodic short spikes. (b) A time series with strong but noisy periodical behavior. TiRex predicts a meaningful uncertainty estimate (quantile range) over the long forecast horizon, while TimesFM and Chronos Bolt struggle because of collapsing quantiles.
Figure 1:
transformers (Merrill & Sabharwal, 2023 Merrill et al. 2024 Delétang et al. 2023). However, they lack strong in-context learning capabilities. To bridge this gap. we adopt xLSTM (Beck et al.] [2024). modern LSTM variant that incorporates architectural enhancements for scalability and improved generalization. particular, XI.STM has demonstrated in-context learning performance comparable to that of wransormer-basee large language models (Beck et al. 2025)
To fully unlock xLSTM's s state-tracking abilities, we introduce Contiguous Patch Masking (CPM), a novel training-time time masking strategy. CPM enhances XLSTM's ability to produce coherent long- horizon predictions by mitigating degradation common in autoregressive multi-step forecasting, as illustrated in Figure
While synthetic datasets frequently used for pre-training forecasting models, the potential of data augmentation strategies remains largely untapped, unlike their established role in vision pre-training (Tian et al. 2020). To address this, we design and utilize suite of augmentations.
Our key contributions are:
TiRex:
We present TiRex, pre-trained time series model based xLSTM, which sets a new state the art in zero-shot forecasting. achieves superior performance across standardized benchmarks, improving both short- and long-term forecasting accuracy.
Contiguous Patch Masking (CPM): We propose novel masking strategy that enhances state- tracktra abilities, therefore enabling pre-trained time series models to produce reliable uncertainty estimates over long prediction horizons, effectively addressing autoregressive error accumulation.
Data Augmentation Strategies: We introduce three augmentation techniques for time series model pre-training and demonstrate their effectiveness in enhancing the robustness and overall performance of TiRex.
After introducing the problem setup and review of related work, the paper is structured as follows: Section Section@iintrduuess TiRex, its architecture, inference strategy, and Contiguous Patch Masking utilized for training. (ectionn3dsscree
the proposed training augmentations. Section Section[evvaluate evaluates TiRex on two standardized real-world benchmarks and examines the impact of the individual components. In Section we discuss limitations of our approach and conclude the paper.
1.1 Problem Setup: Zero-Shot Forecasting
Time series forecasting aims to predict future values of time series based on its past values. Formally, given time series (y1, ./...... .......,7 .,y,, with y: IR denoting the value at time I, the forecasting objective is to predict its future horizon (yr+1, ... //T+h)) where h is the forecast horizon's 's length.

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Throughout the paper, we adopt -yyle array notation and denote a contiguous sequence of values by YI. := (ge) (3/1- .2......... yr) Probabilistic forecasting extends this setup by modeling the uncertainty inherent in most time series data. Instead of producing point estimates, the model learns to approximate the conditional distribution over future outcomes:
P(yr-1-Th Yı.r)
In a zero-shot forecasting setting, the prediction model is pre-trained on a corpus of time series datasets C = {Di, D2,...; Dr). where each D,,, 1 S n S N, is time series dataset, e.g., set of time series from particular domain. At inference the model is applied directly to time series of new, unseen dataset, i.e., y E Djest and y & U? Di, without any fine-tuning or task-specific supervision.
1.2 Related Work
Statistical models such as ARIMA (Box & Jenkins 1968) and exponential smoothing (Hyndman
et al. 2008) are classical approaches in time series forecasting. In the last decades, however, neural network-based models have emerged as effective alternatives: Notable examples include DeepAR
(Salinas et al., 2020), based on a LSTM with a mixture density head; N-BEATS (Oreshkin et al. 2019). the first approach that employed deep block architecture; PatchTST(Nic et al.) 2022). patch-based attention approach; and TFT et al. (02T). which combines LSTM and transformer components. These models are trained on multiple time series from a single dataset and require retraining when applied to new tasks.
Currently, pre-trained time series models, with the capability of zero-shot generalization across datasets, predominantly adopt different transformer architectures. For instance, Chronos (Ansari al. 2024a), Chronos-Bolt (Ansari et al. 2024b), and COSMIC (Auer et al., (025b) use encoder- decoder variant. Moirai (Woo et al. (0024) adopts an encoder-only design with a masked modeling objective, and TimesFM (Das al. (2024) follows decoder-only causal modeling strategy for autoregressive generation. TabPFN (Hollmann et al. (025) and its adaptation to time series TabPFN- TS (Hoo et al. 2023) use modified transformer encoder and pre-train only on synthetic data. A notable exception is TTM (Ekambaram et al., 2024). since it builds on the MLP-based TSMixer architecture (Chen et al. 2023).
The dominance of transformer architectures echoes their strong in-context learning capabilities (an essential property for zero-shot forecasting) which are known from the language domain (Brown) et al. 2020). However, despite their success in language, they often fall short of expectations in time series forecasting. For example, (Zeng et al. (2023) show that DLinear, simple linear model, can outperform transformers in multiple scenarios. Classical models, like LSTMs, are still widely used and remain competitive. While LSTMs are well-suited for time series, they lack strong in-context learning capabilities, Recent advancements in recurrent architectures - such as the xLSTM (Beck) closed this gap. xLSTM shows promise in task specific time series applications (Kraus yet its potential for pre- pre-trained, general-purpose models remains underexplored.
al.
2025)
et al.
2024
2 TiRex
TiRex utilizes xLSTM its backbone architecture, and adopts a decoder-only mode, which allows for efficient training. It stacks multiple xL.TMM blocks between a lightweight input and output layer. The input layer preprocesses the time series via scaling and patching operations, producing tokens that are subsequently processed by the xLSTM blocks. The output tokens correspond to forecasted patches of the target series and are mapped back to the forecast horizon. For multi-patch forecasting, additional inputs are encoded as missing values. An overview of the architecture is provided in Figure 2 with individual components being described in detail below.
XLSTM Block TiRex adpots the block design proposed by Beck et al. (2025). ) but substitutes the mLSTM with sLSTM module as the sequence mixing component. Both module options were introduced in the original publication, but only sLSTM allows for state-tracking (by trading it for reduced memory capacity [Bek et al., (0024). Each block comprises a sLSTM module followed by a feed-forward network, with both components preceded by RMSNorm (Zhang & Senorich] 2019). Additionally, all SL. and feedforward layers include residual skip connections. SLSTM supports real recurrence, enable state-tracking, yet is still efficient in training and inference due to an
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XLSTM Block
Feed
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Forward
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Linear
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Figure 2: Architecture overview of TiRex. The model comprises two main components: the xLSTM blocks and residual block in the input and output layers. The illustrated forecast shows the forecasted series is in blue and the forecast of TiRex in orange. During inference, only the last three output windows of interest.
optimized kernel architecture (Pöppel et al. 2024). TiRex stacks multiple of these blocks, depending on the model size. After the last block, an additional RMSNorm applied. More details on the general xLSTM architecture provided in Appendix
Input/Output Layer and Loss TiRex is designed to generalize across diverse time series domains, which often exhibit significant variation in scale. To ensure robustness, TiRex applies instance normalization to each time series (Kim et al.) 2021). Specifically, z-score normalization is used. That is, Fo.r sample.
Yoer Mo.r where, ÿ and, By denote the mean and standard deviation of the time series dsa.r
TiRex segments time series into con-overlapping windows, and maps each window the input space of the xLSTM using two-layer residual block (He et al. 20116) Srivastava et al.) (015). This patching mechanism inspired by vision transformers (Dosovitskiy et al. 2020) and was adapted for time series by Nie et al. (2022) and Woo et al.) (2024). It reduces the effective sequence length of the XLSTM blocks by a factor defined by the window size. To account for missing values, binary mask indicating presence absence is concatenated to the time series values before the residual block. Given an input window size min and XLSTM hidden dimension the patching block defines mapping 2m. Rd The same residual block is shared across all time windows.
Mirroring the input layer, the decoder's output tokens are transformed back to the dimensions the output-patch window using residual block and subsequently scaled back to the original target space. Hereby, the model outputs provides Q2 quantile values for each time step of the output-pare patch window, rather than angle-point predictions. Hence, the output block defines mapping Rdd - t x [QI1, Specifically, TiRex predicts nine equidistant quantile levels, Q = f0.1, 0.2. 0.9). The model's parameters are optimized by minimizing the quantile loss. The loss is calculated for each output token, therefore, the loss does not distinguish context and forecast for a training sample, but implicitly "forecast after each input token". Formally, the loss for an output window, given the true value y/. at time and its corresponding quantile predictions yi for quantile level g is computed as:
q (y++ 02) (11 (1-9) (0) we
o S
(2)
else
I=1
qEQ
The losses of all output tokens of training sample averaged missing values in the output window are ignored for the loss calculation.
Multi-Patch Horizon Forecasts When the forecast horizon h exceeds the output patch length, multiple future patches must be predicted. We refer to this multi-patch prediction. Existing pre-trained models (Das et al. 2024 Ansari al. 2024b) typically address multi-patch prediction autoregressive generation, using point estimates (say, mean median) of previous outputs inputs for subsequent patches. However, this approach reinitializes the probabilistic forecast at each step, disrupting the propagation of uncertainty. In contrast, TiRex treats future inputs missing values,

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Contiguous Patch Masking (CPM)
Training Augmentation
Batch Targers
MM
TiRex
Censor Augmention
Amplidude Molduation
Spike Injoction
Inpurs
Figure 3: Illustration of Contiguous Patch Masking and the different training augmentations.
allowing the internal memory to propagate both predictive state and uncertainty across patches. This results in more coherent probabilistic and overall better forecasts, as our quantitative and qualitative experiments show (Section and Figure T).
2.1 Contiguous Patch Masking
To facilitate the stable multi-patch prediction capability of TiRex, we propose Contiguous Patch Masking (CPM), illustrated in Figure CPM randomly masks full and consecutive patches in pre-training. Such a masked patch is represented as "missing values" the model input, hence corresponds the structure of the input when multi-patch forecasts used in the inference. The procedure is as follows: For each training sample, we first uniformly sample the amount of consecutive patches Cmask (1, maax and the masking probability Pmask UO, y pmmas) ). Afterwards, we mask the time series: For a time series length T we sample a binary mask of length Giaac with Bernoulli probability Pmask and repeat each element Cmask Mout that the mask has a length of T too. Note that when neighboring elements are masked, the actual maximum of consecutive masked patches can be greater than cmax Further, while CPM incorporates elements from BERT-style (Devlin et al., 2019) masked- modeeddi.odiing,,.. our training is still more similar to the typical causal- style masking of decoder-only approaches (Radford al., (2188) since the target shifted and the information flow umi-directional. Appendix D.4 D.4 provides a sensitivity analysis of the parameters mask and mask'
3 Data Augmentation
To facilitate more diverse time series patterns and enhance the model's exposure to a wider range of potentially relevant dynamics, we propose three augmentations for pre-training. This is inspired by the successful application of augmentation techniques in pre-training of other modalities, c.g., vision (Tian et al. 2020). The employed augmentations, illustrated in Figure 3 are: (1) Amplitude Modulation, which introduces trends and change points in the scale of the time series, Formally, time series y is transformed by si = Vt ag, where a, follows linear trend (potentially with change points). (2) Censor Augmentation, which censors values within the time series at random threshold. The augmented respective series computed by s max/min (yt,, c), The censor threshold is sampled by uniformly drawing a quantile from the empirical distribution of the signal. (3) Spike Injection, which adds short, periodic spike signals to the time series. The augmented time series is computed by vo = + St. where 8; represents the added spike signals. The shape of each spike is defined by a kernel, which can a tophat, a radial basis function (RBF), or a linear kernel. The periodicity and the specific parameters of the kernel (e.g., width, height for tophat; center, variance for RBF) are sampled from predefined distributions for each sample. This randomization is designed to encourage the model to learn general concept of transient events, rather than memorizing specific periodic patterns. The augmentations are applied with a probability of 0.5 for amplitude modulation and censor augmentation and 0.05 for spike augmentation. Appendix B provides more detailed description of the augmentation procedures.
Experiments
This section outlines the experimental setup, including training procedures, evaluation benchmarks, and comparison models. We further report the main results demonstrating the effectiveness of TiRex
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in general (Section 4.1 and the specific components - the xLSTM backbone, Contiguous Patch
Masking, and the proposed augmentations (Section 4.2). Full experimental details are provided in Appendix C while extended results are presented in Appendix D
TiRex Training Our training data comprises three components: (1) We utilize the training datasets
from Chronos (Ansari et al.) (024a), and adopt their TSMixup procedure to augment this data. (2) We enrich our training data with synthetic time series data generated through procedure closely inspired by KernelSynth (Ansari et al. (2024a). (3) We add parts of the pre-training dataset proposed by GiftEval (Aksu et al., 2024). In total, our training dataset encompasses 47.5 million time series samples. Details regarding the specific datasets employed, as well the implementation of the TSMixup and synthetic data generation procedures, can be found in Appendix C.2) During training, we augment the samples with the proposed training augmentations and apply Contiguous Patch Masking as described in Section [ We train TiRex with a context length of 2048 and a window size of 32 for input and output patches.
Evaluation Benchmarks We evaluate TiRex on two standardized benchmarks with public leader- boards: (1) the Chronos Zero-Shot Benchmark" comprising 27 diverse datasets, each in one evalua- tion setting, primarily for short-term horizons (Ansari et al., 2024a). and (2) the GiftEval benchmark (Aksu al. 2024). which includes 24 datasets that are evaluated in different settings, and covers short-, medium- and long-term horizons, as well as different frequencies - in sum 97 evaluation settings. The training data of TiRex has no overlap with this data, hence TiRex operates in zero-shot. We denote this benchmark as Chronos- ZS benchmark. To also ensure zero-shot conditions on the GiftEval benchmark, we exclude 16 of the 97 evaluation settings, which overlap with our training data, and denote this benchmark as GiftEval-ZZ -SS benchmark; complete results for GiftEval are reported in Appendix D.I We note that all Chronos models have the same overlap as TiRex; TimesFM, and Moirai have additional overlapping datasets and additionally also have overlaps with the Chronos-TS benchmark.
The evaluation follows the respective benchmark protocols using mean absolute scaled error (MASE) for point forecast performance and the continuous ranked probability score (CRPS) for probabilistic forecast performance. Practically, the CRPS is approximated by the mean weighted quantile loss (WQL) over nine quantiles: 0.1 to 0.9 in increments of 0. f Aggregated performance is computed by normalizing each evaluation setting's 's score by that of a seasonal naive baseline, followed by the geometric mean across evaluation setting: Additionally, the average rank across evaluation settings is reported to ensure robustness against outlier performance.
Compared Models We compare TiRex against a broad set of state-of ohethe-art models, including
zero-shot pre-trained models and task-specific models. The zero-shot models include Chronos and Chronos-Boll (Ansari et al.) 2024a| b), TimesFM (v1.0, v2.0) (Das et al., 2024), Moirai 1.1 (Woo et al.
2024), TabPFN-TS (Hollmann et al. 2025). and Tiny Time Mixer (TTM) (Ekambaram et al.) 2024). The spsc-fee models are Patch ST (Nie et al. (022), TFT (Lim et al. | 20011). DLinear (Zeng al. 2023), DeepAR (Salinas et al. 2020), and N-BEATS (Oreshkin al. 2019). These models are trained individually on each dataset. Hence, they do not operate in 'ccro-shot" and only provide an asymmetric comparison. Reporting their result is useful to contextualize the current strengths and limitations of zero-shot approaches. We report the results of the public leaderboards if available and replicate the outcomes of pre-trained models within our evaluation pipeline to ensure validity.
4.1 Zero-Shot Forecasting
GiftEval-ZS ZS Benchmark In this benchmark TiRex consistently outperforms all competing methods across both short- and long-term forecasting tasks (Figure 4. In terms of CRPS, TiRex achieves score of 0.411 (with standard deviation over training with 6 seeds of +0.002,, notably surpassing
HuggingFace co/ ctt htts///aacaaasffrrrssrer GIFT-Eval
"In the Chronos ZS benchmark, the mean weighted quantile loss (WQL) is used directly. hence, essentially
both benchmarks evaluate the same metric
*GiftEval benchmark scores are reported based on the leaderboard computation at the time of our submission. A subsequent update to the seasonal naive baseline affects the absolute aggregated scores but does not change any discussed model ranking, result, conclusion.

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Figure 4: Results of the GiftEval-ZS benchmark: Aggregated scores of the overall benchmark and the short- and long-term performances. Additionally, the average rank in terms of CRPS, as in the public leaderboard, presented. Lower values are better. "Zero-shot Leak" refers to models which are partly trained on the benchmark datasets (Overlap:: Moirai 19%, TimesFM 10%, TTM: 16%). We trained TiRex with 6 different seeds and report the observed standard deviation in the plot.
the next best zero-shot models (0.459, 0.463, 0.481). This performance gap is also reflected in the average rank, where TiRex shows substantial lead the second-best model, while the three models that following the ranking (TimesFM-2.0, TabPFN, and Chronos-Boli Bolt-Base) achieve very similar scores among themselves. Importantly, while other models tend peak either in short- (e.g., Chronos-Bolt) or long-term (e.g., TabPFN-TS) forecasting, TiRex is the only model to excel simultaneously both. Moreover, TiRex attains these results with significantly fewer parameters (35M) compared to Chronos-Bolt-Bane
(200M) and TimesFM-220 (500M). The advantage is most pronounced in long-term term-termmmm forecasting, where TiRex becomes the first zero-shot model to surpass the performance of PatchTST and TFT.
Chronos-75, Benchmark The main results on the Chronos-7S benchmark exhibit similar perfor- mance patterns to those observed the GiftEval-ZS benchmark (Figure 5). TiRex again achieves the best results terms WQL score and rank. In the MASE score TiRex has second best score, closely behind TabPFN-TS. Notably, Moirai performs substantially better the Chronos-ZS benchmark (compared to the GiftEval-ZS benchmark). However, this improvement is likely due to the substantial overlap of 82% between its pre-trale pre-training data and the Chronos-ZS test set. These results highlight the robustness of TiRex in zero-shot generalization. The full results, including task-specific models are presented in Appendix D.2
Qualitative Analysis We also qualitatively analyzed the predictions of TiRex and compared them against current state-of-the-art methods. Beyond its generally higher forecasting accuracy, the analysis shows that TiRex demonstrates robust multi-patch prediction capabilities, maintaining coherent uncertainty estimates across different forecast horizons and more accurately forecasts short periodic spikes, which are often missed or smoothed out by other models (Figure and Appendix D.5). We hypothesize that these improvements mainly stem from (i) the effective multi- patch forecasting due to CPM, (ii) the sLSTM architecture that provides state-tracking for uncertainty propagation and strong periodicity modeling, and (iii) the spike augmentation strategy enhancing the model's 's sensitivity to rare, sharp events during training.
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Figure Results of pre-trained model on Chronos-7S benchmark. The aggregated MASE and WOL scores, and the average rank in terms of WQL is shown. Lower values are better. "Zero-shot Leak" refers to models which are partly trained on the benchmark datasets (Over- lap: Moirai 82%, TimesFM 15%, TTM: 11%).
Figure 6: Inference efficiency of the best-
performing pre-trained models. Left: Relation between GPU memory and batch size. Right: Inference time per sample and batch size.
Inference Speed & Memory Apart from the forecasting performance, we analyze the GPU memory consumption and inference runtime across all models. Specifically, evaluate samples with context length of 2048 and a prediction length of 32 over multiple batch sizes. As expected, given TiRex substantially smaller size compared to the next best models (TimesFM-22. --20 and Chronos-Boli Boltt-se-l TiRex requires significantly less GPU memory and achieves faster inference speeds. Specifically, TiRex is over 11x faster than TimesFM-2.0, over 4x faster than Chronos Bolt Base, and over 2176x faster than TabPFN-TS. Furthermore, TiRex even outperforms Chronos- Bolt Small, a similarly sized transformer-basee architecture for larger batch sizes. The differences in maximum GPU memory consumption follow a similar order.
4.2 Ablations
We conduct ablation studies to analyze the impact of key components in TiRex. Specifically, this section focuses on Contiguous Patch Masking (CPM), the proposed data augmentations, and the XL.STM backbone architecture.
Contiguous Patch Masking and Multi-Patch--nferenn We analyze the effectiveness of the pro- posed Contiguous Patch Masking (CPM) procedure by comparing three configurations: (1) standard decoder-only training with autoregressive inference this setting is similar e.g., to TimesFM; (2) training with naive multiple-pate procedure where we place the "rollout" always at the end of the sequence; and (3) training with CPM. Configurations (2) and (3) use the same inference procedure with masked tokens for multi-step forecasting, whereas (1) relies on patch-wise autoregressive de- coding. As shown in Table I only CPM enables strong long-term performance without degrading short-term performance. In contrast, naïve multi-patch training diminishes the short-term forecasting performance, and standard next token training combined with autoregressive inference harms the long-term forecasting performance. These findings suggest that CPM is essential for training and inference behaviors under mulli--ptch prediction.
Augmentation To assess the impact of our augmentations, we trained our model excluding each augmentation and with no augmentations at all. The results, detailed in Table indicate that including the augmentations is beneficial, i.c., improves the performance of the model. Performance consistently decreased in at least one benchmark metric when any single augmentation was removed. The most substantial decline occurs when augmentations were applied. This underscores the effectiveness of each augmentation and their combined positive impact on the model's generalization capabilities. Appendix D.4 provides sensitivity analysis in terms of application probability.
To assess the architectural choice XL. with J.M modules, we replace it with mLSTM (Beck al. 2024) and transformer blocks (Touvron al. 2023) while keeping the patching
Backbone

---

and training procedure unchanged. For the transformer variant, rotary positional embeddings (Su al. 2024) are added to mitigate the absence of inherent positional information, due to their cermutation-invariance property. We also analyze mLSTM and sLSTM mix architectures as proposed in the original XL.TTM paper. We denote xI [ij]] for an architecture where sLSTMM blocks are combined with j mLSTM blocks. Additionally, we ablate our overall architecture by comparing it to a Chronos-Bolt architecture (Base and Small) that we train with our training procedure, using the same datasets and augmentations as for TiRex. Table [ summarizes the results. TiRex with only sLSTM blocks yields the best performance, especially on long-term forecasts. We hypothesize that this is because its explicit state-trace tate--tacking capabilities (Beck et al., 2024), which might facilitate uncertainty propagation and enable accurate modeling of periodic temporal structures over extended horizons. Using only mLSTM performs worst. However, switching just one of these blocks back to sLSTM improves the results close to the SLSTTM-nll architecture of TiRex. The comparison to a Chronos Bolt architecture, which is consistently outperformed by TiRex, highlights that overall architecture is critical to achieve good performance on both long and short-term forecasting. A more detailed comparison the Chronos Bolt architecture is presented in Appendix DD.4
Table 1: Ablation study of individual components. The top two rows report the mean and standard deviation of TiRex over six runs with different random seeds. For the ablation variants, results that degrade performance by more than 3 the standard deviation relative TiRex are underlined. Columns correspond to evaluation settings: GiftEval-ZS benchmark (overall, short-term, and long- term) and Chronos-7S benchmark. Lower values indicate better performance.
Benchmark
Gift-ZS Overall CRPS
Gift-ZS Long MASE
Gift-ZS Short MASE
Chronos- MASE
MASE
CRPS
CRPS
WQL
TiRex
0.411
0.647
0.325
0.45
0.455
0.696
0.592
0.776
16 seeds
0,002
0.004
0.003
0.003
0.001
0.004
0.007
0.003
naïve
CPM
0.424
0.662
0.335
0.460
0.475
0.718
0.650
0.817
multi-patch
w/o multi-patch
0.445
0.704
0.370
0.518
0.471
0.719
0.589
0.777
w/o any
0.430
0.682
0.339
0.478
0.473
0.722
0.623
0.800
Augment
w/o censor
0.417
0.652
0.336
0.457
0.458
0.699
0.595
0.767
w/o spike
0.415
0.660
0.328
0.459
0.462
0.710
0.591
0.773
w/o amplidude
0.409
0.644
0.323
0.448
0.455
0.694
0.618
0.798
modulation
Transformer
0.422
0.662
0.342
0.472
0.461
0.702
0.597
0.768
Backbone
mLSTM
0.457
0.718
0.430
0.589
0.456
0.699
0.588
0.775
[.STM[1:11]
0.414
0.652
0.330
0.456
0.455
0.698
0.631
0.807
XLSTM[1:5]
0.412
0.651
0.330
0.460
0.450
0.693
0.611
0.791
Chronos Bolt S
0.456
0.676
0.413
0.498
0.463
0.705
0.609
0.791
Chronos Bolt B
0.454
0.670
0.418
0.493
0.458
0.701
0.627
0.807
Conclusion
This work introduces TiRex, a pre-trained time series forecasting model based on xLSTM. To fully unlock the state-tracking capabilities of xLSTM, we further propose Contiguous Patch Masking, training-time masking strategy tailored for in-context learning. Contiguous Patch Masking is crucial component in our modeling pipeline, since it enables strong long-term forecasting performance without sacrificing short-term capabilities. TiRex establishes a new state-of-the-art in zero-shot capabiids forecasting, outperforming prior methods on both short- and long-term horizons across the Chronos- ZS and GiftEval benchmarks. Our ablation studies highlight the individual contributions of each component to overall performance.
Limitations & Future Work Like most pre-trained forecasting models, TiRex focuses on univariate time series. Although modeling multivariate series as independent univariate signals often performs well reflected in the Gil results and, for example, shown in Nie al. (2022) future

---

work could incorporate multivariate data, for example in the form of extended contexts or modified input layers. Due computational constraints, we did not extensively tune hyperparameters and only conducted a sensitivity analysis on key parameters. Future work should explore more comprehensive tuning for additional performance gains and investigate leveraging the model's learned representations for other downstream tasks, such as classification (Auer et al. 2025a) or anomaly detection.
Acknowledgments and Disclosure of Funding
We thank Maximilian Beck and Korbinian Pöppel for the discussions and advice with regard to XLSTM. We thank Elias Bürger, Bernhard Voggenberger, Marco Obermeier, and Levente Zolyomi for their efforts in providing an updated TiRex 1.1. We thank Martin Loretz for making TiRex run efficiently on CPU. The ELLIS Unit Linz, the LIT AI Lab, and the Institute for Machine Learning are supported by the Federal State Upper Austria.
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Appendix
Table of Contents
XLSM
Data Augmentation
16
C Experiment Details
18
Model and Training Hyperparameter
18
Pre- Training Data Corpus
18
Benchmarks and Metries
21
C.4 Computation & Hardware
22
D Extended Results
25
D.J Full GiftEval leaderboard
25
D.2
Zero-Shoo Shot Forecasting
25
Multivariate datal
26
D4
Ablations
30
D.5
Additional qualitative examples
32
D.6
Finetuned-Forecastinng
32
E TiRex I.I Full GvltEval Zero-Shof
32
Socictal Impact
33
G
Code
33
A xLSTM
TiRex utilizes XLSTM (Beck et al. 2024) as its backbone architecture. xLSTM extends the classi- cal LSTM (Hochreiter 1991 Hochreiter & Schmidhuber 1997) by incorporating modern design principles to improve its scalability, parallelization, and in-context modeling capabilities.
XLSTM introduces two cell types: the matrix LSTM (mLSTM) and the scalar LSTM (sLSTM). The mLSTM designed to increase memory capacity through a matrix-bas based memory representation, and enables efficient parallel computation. In contrast, the sLSTM preserves true recurrent pathway as in the original LSTM, enabling strong state-tracking capabilities (Beck al. 2024). The recurrent pathway makes L.TTM more expressive than State Space Models (SSMs), parallelizable RNNs like RWKV, and transformers (Merrill & Sabharwal] 2023; Merrill et al. 2024 Delétang et al. 2023). Figure 7 illlustraees the respective expressivity hicrarchies. We hypothesize that this advantage in expressivity allows TiRex to better model complex temporal dynamics, leading to improved forecasting performance, especially over long horizons. [Delétang et al. (2023) demonstrate on synthetic language tasks that this state-tras taate-tracking capability LSTMs yields empirical advantages. Beck et al. (2024) show that sLSTM retains these advantages. sLSTM employs multi-heat strategy along the recurrent pathway to improve efficiency.
TiRex exclusively employs sLSTM cells. Given sequence of T embedded input patches X1.7 (m),, .., aT) E RdxT the forward computation of an sI.STM cells for a given time step defined as follows:
14

---

c = c
+ 1 2t.
cell state
(3)
nu f ② n + it
normalizer state
(4)
h Ot h
h Ct ④ nr
hidden state
(5)
(Ex)
Σ. Wz at
+ R₂ h4-1 + bz
cell input
it exp ir
i. Wi Et
Ri h:-1 + b
input gate
f, exp
f
f, Wr + RS h + b
forget gate
(8)
(o:)
6, W. T. + Ro h + bo
output gate,
where he E Fdd denotes the hidden state, a normalizer state. Further, 1, O₁, f E I2 are the input, output and forget gate, respectively, W.. W,, Wr, W. Rdx R2 Rí. Rr, R. E Rddd and b2, by by, b. E R are trainable weight matrices and biases. The matrices Rz, R; Rg. R. are block-diagonal, where each block represents one head. This way, the parameters reduce to d /(Nr), where N₁, is the number of heads, limiting the cell interactions to individual heads. The input-, output-, and forget-gates are activated by exponential (exp) sigmoid functions (o); The cell inputs use hyperbolic tangent function (p).
Rd denotes the cell states and, nu E Rd denotes
To enable deep modeling, XLSTM organizes its recurrent layers into blocks that combine sLSTM and/or mLSTM layers with additional architectural components. Specifically, TiRex uses the block structure from Beck et al. (2025) that consists
1. an sLSTTM module
2. feed forward network
3. residual connections around each subcomponent,
4. and pre-normalization layers (RMSNorm)
This block architecture is illustrated in Figure 2 and allows for the training of deep networks. To achieve scalability, xLSTM employs custom CUDA kernels that enable high high-throughhut training and inference on modern hardware (Pöppel et al. 2024).
infinite
recursively enumerable
context-semsition
RNN
linear tape
deterministic context frre
Suck-ANN
regular
stack
RNN
finite
FRNN Tiansformee
finite-state
counter
Grammar type (low + high)
Automaton
Memory
Regular (R)
Finite-state automaton (FSA)
Automaton state
Context-free (CF)
Push-down automaton (PDA)
infinite stack
Context-sensitive (CS)
Linear bounded automaton (LBA)
+ bounded tape
Recursively enumerable (RE)
Turing machine (TM)
infinite tape
Figure 7: Formal language classes and their correspondence with neural network architectures and k-counter machines that have counting mechanism (from: Delétang al. 2023).
15

---

B Data Augmentation
This section details the time series augmentations proposed and used for pre-training TiRex.
Amplitude Modulation This augmentation introduces scale trends and change points into the time series by multiplying the signal with a piecewise linear trend. The modulation trend is generated by sampling change points and interpolating amplitudes between them. See Algorithm I
Censor Augmentation This augmentation censors (clips) the input signal either from below or above, depending on a randomly sampled direction. The clipping threshold is determined by drawing a quantile uniformly from the empirical distribution of the signal. See Algorithm [
Spike Injection This augmentation injects structured additive signal in the form of sparse, periodic spikes. First, a periodic pattern is sampled, which is then tiled across the time axis with a sampled periodicity. Each spike label in the pattern is mapped to kernel (selected from fixed set) with randomized parameters that control shape and magnitude. The final augmentation the sum of all such kernel evaluations added to the original signal. See Algorithm The goal of this augmentation to improve generalization to sharp, transient events by exposing the model to diversity spike structures. The spike kernel types and their parameter ranges are defined in Table 2 while the available temporal patterns and their sampling probabilities are described Table
Algorithm 1:
Amplitude Modulation
Input: Time series y IRT
Output: Augmented time series Yaug
k (ni 5)
// Number of changepoints
2 Sample & changepoints {ci,.... c C (l,... Cl,...,T-11]
[0, sorted (ci,... ..c....,,... (,,), T):
Sample amplitudes
(1, ([[1,))++ 12
Interpolate trend e IR from (c,a):
Yaug { @t;
7 return Yang
Algorithm 2: Censor Augmentation
Input:
Time series y E TR.
Output: Augmented time series y Yaug
Sample quantile level q ~ Uniform (0, 1):
Compute threshold t Quantilc(y, q)
3 Sample censor direction b (0.))
// Bottom or top censor
if b then
Yang < max(ye, e) all L:
// Bottom censoring
else
L Youg + min c) for all t;
// Top censoring
return Yaug
16

---

Algorithm 3: Spike Injection
Input: Time series E IR' spike patterns P, spike kernel set IC
Output:
Augmented time series Yaug U(10, m5n, :
Sample periodicity
2
Sample periodic pattern 2 E P and shift it randomly;
Sample U(T x, ;
Generate spike positions
Zd by repeating with spacing and shifting align last spike
8;
Sample kernel type x E KC;
6 For each unique spike label in m, sample kemnll parameters and generate kernel centered at each occurrence:
Sum kernels obtain additive spike signal E R²;
Yaug f- + s:
return Y.ug
Table 2: Kernel types and parameterizations (as functions of the periodicity x) employed for the spike injection augmentations
Kernel
Width Param
Amplidue Param
Tophat
[0.05x, 0.2x]
h h [0.5,
RBF
ØBBF [0.05 0.2m]
h ~ 00.5, 3
Linear
[0.05 0.2
h [0.5,3 3
Table 3: Spike pattern, representative patterns, and sampling probabilities employed for the spike
injection augmentations.
Category
Utilized Pattern
Sample Probability
Simple
00, [0,
0.75
3-periodic
0, 0, 0,0,
0.10
4-periodic
0, 1,
0.10
Weekly-like
00.000000111110000000000 0,0,0,0,,111
0.05
17

---

C Experiment Details
C.1 Model and Training Hyperparameter
TiRex utilizes a XLSTM-based architecture with hyperparameters summarized Table 4 The model has 35 million model parameters.
Pre-Traines Pre-Training TiRex is pre-trained for 500,000 steps with a batch size of 256 using the Adam optimizer with learning rate of 0.001 and weight decay of 0.01. We also employ cosine learning rate scheduler with linear warm-up (the warm-up ratio is set and the minimum learning rate is 0.0001). The context of TiRex length is 2048.
Table 4: TiRex model architecture hyperparameters.
Parameter
Value
Input patch size (m²)
32
Output patch size (Mom)
32
Embedding dimension (d)
512
Feed-forward dimension (dg)
2048
Number of heads
Number of blocks
12
C.2 Pre-Training Data Corpus
We construct diverse training corpus by combining real and synthetic time series to support robust generalization across heterogeneous forecasting tasks. Our training dataset has three components:
1. Chronos Training Data (30 million time series): We incorporate the training datasets from Chronos and adopt their proposed time series mixup augmentation strategy (Ansari) et al. 2024a).. In contrast Chronos, generate significantly more and longer time series, expanding the diversity and temporal span of the data. Table the respective datasets, which are provided HuggingFace:
Btapp::///Hgginghhe acee. ctt co/datastts/ chronosddatasets datasets Details on the TsMixup procedure are provided in the
autogluon/ chronos paragraph below.
2. Synthetic Gaussian Process Data (15 million time series): Inspired by KernelSynth (Ansari et al. 2024a), we generate synthetic time series using Gaussian Processes (GPs). Details on the synthetic data generation procedure are provided in the paragraph below.
3. GiftEval Pre-training Data (+= 2.5 million time series): We integrate a subset of the pre-
training corpus from GvftEval and use it for pre-training. It does not overlap with the GvftEval benchmark evaluation data. Table 6 lists the respective datasets, which are provided on Hug- gingFace: https: Ttttps://Hugiinn httg///ugggggggg Face. co/ http///aatttslleeeeeeee/eetaaaaa
train
Data Mix Probabilities For the Chronos training data and the synthetic Gaussian process data, each time series is sampled with equal probability. The GiftEval Pre-training data is sampled with probability of approximately 8%, hence slightly oversampled compared to the share of series due to technical implementation details.
TsMixup To augment data diversity, we apply TsMixup (Ansari et al., 2024a). a convex com- bination of le time series of length 1 to the training data from Chronos. Each series is 2-score normalized (Chronos used mean normalization) prior to combination to ensure comparable magni- tude. The number & is sampled uniformly from {l.... Kmax): ). the length / is sampled uniformly from [Iming [mma], and the mixing weights X are drawn from a Dirichlet distribution:
mix
A &
(10)
where &; R is a normalized time series segment, À Dir(a). As sampled with non-zero probability, the augmented dataset includes original sequences, thereby preserving base
18

---

data fidelity while enhancing variability, In our procedure we utilize Kmax 4, Liin 128, Liin 4096, and a 1.5; we generate 30 million time series.
Synthetic GP Data We generate synthetic time series using Gaussian Processes (GPs), building upon the core ideas of KerneSyynth (Ansari al. 2024a). Each synthetic time series R Tooe is sampled from GP:
X CP(O, R(L,
(11)
where ((t,t') is composite kernel constructed by randomly sampling and combining kernels from a kernel bank K. We sample j ~ U( J} base kernels (with replacement) from K. and combine them using random binary operations from {+, x} to obtain Kemel parameters (e.g., length scale, periodicity) are sampled from predefined priors. In our procedure, we utilize J = 4 and Lyya = 4096; Our kernel bank K. includes periodic, Radial Basis Function (RBF), Rational Quadratic (RQ). and Piecewise Polynomial kernels. We generate 15 million time series with this procedure.
In contrast to Kemellyyth, we introduce the following adaptations:
1. We sample periodicities from both fixed sets (as KerneISynth) and additionally from contin- uous distributions to increase temporal diversity.
2. We employ more scalable GP sampler with GPU support and approximations for longer series (Gardner et al. 2018). This enables the generation of more and longer sequences.
3. We use modified kernel bank.
Table 5: Training Datasets published by Ansari et al. (2024a) btctps://huggingeee co/ that were utilized to train TiRex.
datasets/ nuttgluunn/chrooo..ooooo
Name
#Series
Avg. Length
Mexico City Bikes
494
78313
Brazilian Cities Temperature
12
757
Solar (5 Min.)
5166
105120
Solar (Hourly)
5166
105120
Spanish Energy and Weather
66
35064
Taxi (Hourly)
2428
739
USHCN
6090
38653
Weatherbench (Hourly)
225280
350639
Weatherbench (Daily)
225280
14609
Weatherhench (Weekly)
225280
2087
Wiki Daily (100k)
100000
2741
Wind Farms (Hourly)
100000
8514
Wind Farms (Daily)
100000
354
Electricity (15 Min.)
370
113341
Electricity (Hourly
321
26304
Electricity (Weekly)
321
156
KDD Cup 2018
270
10897
London Smart Meters
5560
29951
M4 (Daily)
4227
2371
M4 (Hourly)
414
901
(Monthly)
48000
M4 (Weekly)
359
1035
Pedestrian Counts
66
47459
Rideshare
2340
541
Taxi (30 Min.)
2428
1478
Temperature- Rain
32072
725
Uber TLC (Hourly)
262
4344
Uber TLC (Daily)
262
181
19

---

Table 6: Subset of pre-trainne pre-training datasets published by Aksu et al. (2024)
(https: hettps://huggingfaas
co/
esf ottttaattttsssleeeeeerraaaaaaala
that utilized train TiRex.
Name
#Series
Avg. Length
azure vm traces 2017
159472
5553
borg cluster data 2011
143386
3749
bdg-2 panther
105
8760
bdg-2 fox
17219
bdg- rat
280
16887
bdg-2 bear
91
16289
Icl
713
13385
smart
5
19142
5785
sccaux
34223
borealis
15
5551
buildings 900k
1795256
8761
largest 2017
8196
105120
largest 2018
8428
105120
largest 2019
8600
105120
largest 2020
8561
105408
largest 2021
8548
105120
PEMS03
26208
PEMS04
307
16992
PEMS07
883
28224
PEMS08
170
17856
PEMS BAY
52128
LOS LOOP
207
34272
BELIIGG SUBWAY 30MIN
276
1572
SHMETRO
288
8809
HZMETRO
80
2377
Q-TRAFFIC
45148
5856
subseasonal
862
16470
subscasonal precip
862
11323
wind power
7397147
solar power
7397222
kaggle web traffic weekly
145063
114
kdd2022
134
35280
godaddy
3135
41
favorita sales
111840
1244
china air quality
437
13133
beijing air quality
12
35064
residential load power residential pv power edc fluview ilinct
271
538725
233
537935
75
852
edc fluview who
74
564
20

---

C.3 Benchmarks and Metries
We evaluated our models on two standardized benchmarks, GiftEval (Aksu et al. 2024) and the Chronos Zero-Shot benchmark (Ansari et al., (024a)). Both are hosted on public HuggingFace leaderboards. These benchmarks offer transparent, reproducible evaluations across a wide range of datasets, domains, and forecast horizons, enabling comprehensive assessment of generalization capabilities. The benchmarks not only specify the datasets and forecast horizons but also metric computations, and provide results of Mate-of-the-art models, ensuring valid baseline comparisons.
GiftEval. GiftEval (Aksu et al. 2024) comprises 23 datasets totaling over 144,000 time series, spanning seven domains, ten sampling frequencies, and a wide range of forecast horizons from short- to long-term. sum the benchmark evaluates 97 different evaluation settings. The benchmark includes evaluations of 17 models, covering classical statistical methods, deep learning approaches, and recent foundation models, including all pre-trained models relevant to our study.
In total, 16 out of the 97 evaluation settings in GiftEval overlap with those used for pre-training in our work (i.e., the Chronos pre-train collection). To ensure comparability while avoiding data leakage, we restrict our main evaluation to non non-overlapping datasets. We denote this benchmark as GiftEval-ZS benchmark. This is possible because of the dataset-level granularity of the leaderboard submissions, which allows custom aggregations of results while preserving fidelity to the original benchmark. Full benchmark results, including the overlapping datasets, are reported in Appendix [D.]] The individual datasets and evaluation settings of the benchmark are listed in Table 8 For additional details, please refer to Aksu et al. (2024).
GvftEval uses the Mean Absolute Scaled Error (MASE) for point forecasts and the Continuous Ranked Probability Score (CRPS) for probabilistic forecasts as performance metrics. Equation [2] defines the MASE: Dt is the point forecast, y/: is the observed value at time t. MASE scales the error by naïve seasonal forecast, given the seasonal period s. Equation]] 13 respectively defines the CRPS: F(u) is the predictive cumulative distribution and 1 I u) is the indicator function for the observed value. To evaluate performance over a full forecast horizon, the CRPS is averaged across time steps. In practice, CRPS is approximated by computing the average weighted quantiles loss over a fixed set of quantile levels Q- {0.1,0.2, 0.2,........000 0.9), with o as the quantile prediction of quantile at time step / (see Equation 14.
1 T4t
h Σ
-+= T+1 10: 3el
MASE
(12)
R 2t
2t= s+1 18/e V/t-ol
1 T+h
CRPS = h I=
Σ
(F(u) 1186 S &u})² du
(13)
2
T T+h +1=++1 (q. 02 (1)
CRPS ~ 1Q1 h Σ
(14)
Eter+ lyel
9EQ
( 1(11=- - 088
if 1l S yt.
QL (gg. = (11 () yt))
(15)
else
Before aggregation, the metric values of both metrics are normalized per dataset using a seasonal naive baseline to mitigate scale effects. The aggregated metric scores are computed using the geometric mean of these normalized scores. Additionally, the average rank of the CRPS across evaluation settings is reported to increase robustness against outlier results. Gvf benchmark scores are reported based on the leaderboard computation at the time of the submission. A subsequent update to the seasonal naive baseline affects the absolute aggregated scores but does not change any discussed model ranking, result, or conclusion.
Chronos-ZS benchmark. The Chronos-7S benchmark (Ansri et al. 2024a) consists of 27 datasets, with a focus on short-term forecasting. TiRex's 's pre-training data has no overlap with Chronos-7S benchmark, hence we can use it to extend the assessment of its zero-shot capabilities. The evaluation
21

---

metrics are identical in structure to GiftEval: MASE for point forecasts and Weighted Quantile Loss (WQL) for probabilistic forecasts, with WQL evaluated over the same it computationally equívalent to the CRPS approximation of GiftEvvl.. Aggregation procedures, including baseline normalization and geometric mean computation, are also consistent across both benchmarks. The datasets and settings of the benchmark are presented in Table g for additional details, please refer to Ansari et al. 2024a).
quantiles, making
C.4 Computation & Hardware
We conducted all experiments on Nvidia A40 and H100 GPUS - A40's provide enough GPU memory to conduct all training runs. The inference experiments (GPU memory and Inference Speed) were conducted on Nivida A40 GPU. CPU requirements are flexible; we utilized 64-core Xeon(R) Platinum 8358.
22

---

Table 7: GiftEval (Aksu et al. 2024) benchmark datasets and evaluation settings, Evaluation settings that are part of GiftEval-ZS benchmark are marked in the respective column. Forecast Horizion abbreviated as "Hor" and the number of evaluated windows is abbreviated as "Win".
GiftEval-ZS
#Series
Freq
Short
Medium
Long
Name
Hor
Win
Hor
Win
Hor
Win
bitbrains fast_attssostt____a storage
5T
1250
48
18
480
2
720
2
bitbrains fast_ storage
H
1250
48
bithrains_ma
500
48
18
480
2
720
2
bithrains_ma
H 500
48
2
bizitobs_app appliicaion
10S
60
15
600
2
900
I
bizitobs 12c
ST
48
20
480
7
720
5
bizitobs
H
48
720
bizitobs _eziiobs_service service
1OS
21
60
15
600
2
900
car car_parts covid_deaths deaths
M
2674
12
D
266
30
electricity
1ST
370
48
20
20
electricity
D
370
electricity
H 370
48
20
480
8
720
5
electricity
W 370
8
ettl
1ST
48
20
480
15
720
10
ettl
D
ettl
H
48
20
480
4
720
3
ettl
W
8
ctt2
1ST
48
20
480
15
720
10
ett2
D
30
HH
W
48
20
720
elt2
8
2
DN
hierarchical sales
206
30
4
WWW
hierarchical sales
118
8
hospital
767
see_heethhrr
LOT
48
20
480
11
720
8
jena_weather
D
30
mea_heether
H
48
19
480
2
720
2
D
270
30
kdd cup 2018
H 270
48
20
loop seattle
ST 323
48
20
480
20
720
15
loop_seattle seattle
D 323
30
loop_scattle
H 323
48
19
480
2
720
2
m4_ m4_daily
D
4227
m4 m4_hourly
H 207
48
2
m4 m4_monthly
M
2400
18
20
m4 mq_uuarterly
OO
24000
8
m4 m4_weekly
359
13
MARERA
m4 yearly
22974
6
m dense
30
30
dense
30
48
20
480
4
720
3
restaurant
403
30
saugeen
30
20
saugeen
saugeen
W
8
20
solar
LOT
137
48
20
480
720
8
solar
D
137
30
solar
I
137
48
19
720
solar
W
137
8
sz_taxi
1ST
156
48
7
480
720
sz_ saxiaxi
156
48
2
temperature_ rain
32072
30
births
20
us birthiits
12
2
us. births
W
8
14
23

---

Table 8: Chronos-Ze ZS benchmark benchmark datasets (Ansrii et al. 2024a) and evalution setting.
Name
Horizon
Periodicty
traffic
australian electricity
48
48
eтсоt
24
24
ETTm
24
96
ETTh
exchange rate
5
nn5
56
1
nn5 weekly
8
weather
covid deaths
1
fred md
12
m4 quarterly
8
4
m4 yearly
6
dominick
m5
1
tourism monthly
24
12
tourism quarterly
8
4
tourism yearly
car parts
hospital
12
12
cif 2016
12
12
ml yearly
6
1
quarterly
4
ml monthly
18
m3 monthly
18
12
m3 yearly
6
1
m3 quarterly
4
24

---

GiftEval Agg Score (sarted by CRPS)
GiftEval
Gif.Eval Full
Aug
Agg
(sorted CRPS)
Long Term
Chronos Bolt
TabPFN-TS
TiRex
2.0
0.42. 0.002
0.46
0.48 0.75
0.49
0.65+ 0.003
0.68
Chrenos
TimesHM
TabPEN-TS
TiRex
3.0
6.1
5.0
6.0
PatchTST
Tir ex
TFT
0.34+
D.37
0.38
0.48 0.003
0.003
0.59
Chronos Boll 5
PStchTST
0.49 0.74
0.50
Chrones Bolt
Moiral L 1.1
7.2
TimesFM 2.0
TabPFN-TS
0.4
0.53
0.59
Moiral 1.1
0.79
Moiral 8 1.1
7.4
Moirai L11
0.42
TFT
0.82
PatchTST
7.4
Moirai
0.81
TFT
8.2
Short Term
Chronos
0.55 0.79
0.56 0.80
TimesFM
10.2
10.2
TIR
0.46:
0.69 0.00
TimesFM 1.0
N-Beats
DLinear
0.57
D.73 0.95
00.7
Chronos
DecpAR
N-Beats
14.1
Chronos Bolt B
Chronos Bott s
TimesFM 2.0
0.49
0.50
0.70
0.74
DeepAR
0.72
Auto ARIMA
14.8
TapPFN-TS
0.51
0.75
TTM-r2
0.74
0.74
0.92
TTM-2
15.1
Chrones
0.77
Auto ARIMA
0.77
0.96
DLinear
15.1
0.00
0,25 Zero-Shot
0.50
0.75
1.00
1:88
Theta
15.8
17.2
Shol
Specific
Local
CRPS
0.0
0.5
1.0
10
20
Figure 8: Results of the full GiftEval benchmark: Aggregated scores of the overall benchmark and the short- and long-term performances. Additionally, the average rank in terms of CRPS, as in the public leaderboard, is presented. Lower values are better. "Zero-shot Leak" refers to models which are partly trained on the benchmark datasets. We trained TiRex with different seeds and report observed standard deviation in the plot.
D Extended Results
This section presents additional experimental results complementing Section 4 The structure the same as in the main paper. preceded by results for the full GiftEval benchmark: First, extended results on the zero-shot evaluation of GiftEval-ZS benchmark and Chronos-ZS benchmark are presented, followed by inference efficiency results of all pre-trained models, extended ablation studies results, and additional qualitative examples. Additionally, we provide fine-tuning results.
D.1 Full GiftEval leaderboard
Figure presents the evaluation results on the full GiftEval benchmark, including settings excluded from GiftEval-ZS benchmark due to training data overlap with TiRex. These results align with those reported on the HuggingFace GiftEval leaderboard. The results are consistent with the trends observed in the main GiftEval-ZS benchmark evaluation. TiRex outperforms all baseline models by substantial margin, with the largest performance gap observed in the long-ten term forecasting tasks.
D.2 Zero-Shot Forecasting
GiftEval-ZS benchmark Figures 9 present the short-, medium-, and long-term evaluation sub-results for all models. Both aggregated scores and average CRPS rank metrics are reported. As discussed in the main text, TiRex consistently achieves the best performance across all settings. The results of the individual evaluation settings are reported in the Tables 16
Chronos-ZS benchmark Figure 12 extends the Chronos benchmark results by including task- specific and local models not covered by the official leaderboard, which reports only pre-trained models. These additional results are taken from the benchmark's original publication (Ansari et al.) 2024a). Consistent with the main paper, TiRex performs best and even outperforms models with substantial training data overlap and those explicitly trained individual datasets. The results the
individual evaluation settings are reported in the Tables 17 18
25

---

Inference Efficiency Figure 13 presents an extended inference efficiency comparison, including additional pre-trained baselines beyond those shown in the main paper.
D.3
Multivariate data
While TiRex models each time series variate independently. this approach remains remarkably effec- tive on multivariate forecasting tasks. This observation consistent with previous work demonstrating that strong univariate models can serve as powerful baselines multivariate benchmarks (e.g., Nie al. 2022). Our main results on the full GiftEval-ZS benchmark, which contains 8 multivariate datasets, already support this, as TiRex outperforms several multivariate models.
To make this point explicit, Table 14 isolates the performance only the multivariate subset of the GiftEval-ZS benchmark benchmark. Even in this setting, TiRex achieves the top rank among models designed specifically for multivariate forecasting (e.g., Moirai, TTM).
GiftEval 25
long Agg Score
GiftEval ZS lang Avg CRPS Rank
TiRex
0.3
0,003
TiRex
2.3
PatchTST
0.35
PatchTST
4.8
TFT
0.36 0.55
TFT
TabPFN-TS
0.39 0.55
TimesFM
0.48.45
Moiral
6.8
0.56
Moirai 6
7.5
Mcirai
TimesFM 2.0
7.6
Chronos Bolt 9
0:42 0.55
Chronos Bolt
Chronos Belt
0142
0.49
Chrones Bolt
0.66.6
11.9
TimesFM
1.00
TimesFM
12.1
Chronos
0.5
DeepAR
12.3
TTM+2
0.5660
N-Beats
12.4
DLinear
0.5*0.65
Chronos
N-Beats
0
1.00
13.1
Auto ARIMA
0. 0.99
Auto ARIMA
16.0
Seas, Naive
1:00
Seas. Naive
16.6
Auto Theta
0.82
1.
Auto Theta
17.0
0.0
0.4
0.6
0.8
1.0
1.2
1.4
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
Zero
Zero-Shot Leak
Task Specific
Local
CRPS
Figure 9: Results of the GiftEval-7S benchmark: The aggregated scores and the average CRPS rank of the benchmarks' long-term sub-results are shown. Lower values are better. "Zero-shot Leak" refers to models that are partly trained on the benchmark datasets. We trained TiRex with 6 different seeds and report the observed standard deviation of the aggregated scores.
26

---

GiltEval 25 medium Agg Score
Girteval 25 medium Avg CRPS Rank
TiRex
0.40: 0.004
0.77:
TiRex
PatchTST
0.45
0.86
TFT
TFT
0.45
0.96
PatchTST
TimesFM
0.48
0.82
TabPFN-T5
6.3
TabPFN-TS
0.48
0.95
Moirai
6.7
Meirai 1.1
0.97
TimesFM 2.0
7.1
Chronos Bolt
0.52
Moiral B 1.1
7.6
Moirai 1.1
0.52
1.03
Chronos
Chrones Belt
0.53
0.95
DeepAR
0.59
1.28
DeepAR
10.7
Chranes
1.08
TimesFM 1.0
11.6
TimesFM 1.0
0.62
Chronos
12.2
Chronos
0.62
1.08
Chronos
12.7
N-Beats
0.65
1.03
N-Beats
0.65
1.09
14.1
1.05
TTM-1
14.2
Auto ARIMA
Auto ARIMA
15.9
Seas. Naive
Seas. Naive
16.4
Auto Theta
1.18
Auto Theta
0.00
0.25
0.50
0.75
1.00
1.25
1.50
0.0
2.5
5.0
10.0
12.5
15.0
Specific
CRPS
MASE
Figure 10: Results of the GiftEval-ZS benchmark: The aggregated scores and the average CRPS rank of the benchmarks' medium-terge sub-results are shown. Lower values are better. "Zero-shot Leak" refers models that are partly trained the benchmark datasets. We trained TiRex with 6 different seeds and report the observed standard deviation of the aggregated scores.
GiftEval ZS shart Agg Score
GiftEval Z5 short- Avg CRPS Rank
TiRex
0.45 * 0,001
0.70
TiRex
TimesFM 2.0
0.48
Chrones
Chronos Belt
0.49
0.75
TabPEN-TS
0.49
0.75
TabPFN-TS
3.6
Chronos Bolt
0.49
0.75
TimesFM
5.6
Moirai
Mairai B 1.1
7.2
Moiral 1.1
0.53
Mairal L 1.1
7.5
Chronos
0.33
0.78
Chronos
01.4
0.78
0.82
TimesFM
9.4
TFT
0.86
Chronos
9.4
TimesFM 1.0
TFT
9.8
N-Beats
0,71
0.84
DocpAR
Auto ARIMA
0.73
0.94
DeepAR
0.76
1.19
14.6
DLincar
1.02
Auto Theta
14.8
Auto Theta
DLinear
15.8
TTM-2
0.84
TTM-2
16.3
Seas. Naive
1:88
Seas, Naive
0.4
10.0
12.5
15.0
Zero-Shot
Specific
MASE
Figure 11: Results of the GiftEval-ZS benchmark: The aggregated scores and the average CRPS rank of the benchmarks' short-term sub-results are shown. Lower values are better. "Zero-shot Leak" refers models that are partly trained the benchmark datasets. We trained TiRex with 6 different seeds and report the observed standard deviation of the aggregated scores.
27

---

Chroncs-22 Z5 Agg Scores (sarted by WQL)
Chronas-25 Average Rank WQL
TiRex
0.59
0.78 0.003
0.007
TiRex
5.4
Moirai
0.62
0.78
TabPFN-TS
6.9
Chronos
0.62 0.79
Chronos Bolt
7.4
TabPFN-TS
0.662 0.77
Moirai L 1.1
7.8
Bolt
0.63 0.82
TFT
7.9
0.81
PatchTST
8.1
0.85
Times 2.0
8.2
Moirai
0.64 0.81
N-Beats
8.5
Chrones
0.65 0.83
Moirai B
8.6
PatchTST
0.81
Chronos Bolt
18.7
0.7 0.83
DeepAR
9.4
TimesFM
0.71 0.71.00 0.80
Chronos
10.2
TimesFM
0.88
Times 1.0
10.4
DeepAR
6.72 0.84
Auto Theta
11.3
ARIMA
0.74
Chronos
11.3
DLinear
0.76
Auto ARIMA
11.6
Auto Theta
0.80
DLinear
13.0
Seas. Naive
1.88
Seas. Naive
173
TTM-r2
1.05
TTM-2
17.6
0.0
0.2
0.4
0.6
0.8
1.0
5
10
Zero Shot
Zero-Shot Leak
Task Specific
Local
MASE
Figure 12: Results of the Chronos-ZS benchmark: The aggregated scores and the average WQL rank. Lower values are better. "Zero-shot Leak" refers to models that are partly trained on the benchmark datasets (Overlap: Moirai 82%, TimesFM 15%, TTM: 11%). We trained TiRex with different seeds and report the observed standard deviation of the aggregated scores.
GPU Memory
Sample
1000.0
500.0
34
29
100.0
Max Memory (GB)
24
50.0
20
Time
10.0
15
5.0
5-
0.5
0.0
23
2
2
2
2/
2.0
23
24
27
2
2/
240
Batch Size
Batch Size
TiRex
Chrones Chronos
TimesFM
-a- TTM-2-22
Molrail.18
Chronos-Bolt B
TimesFM 2.0 wa- TabPFN-TS
Moirail.1
Chrones-Bolt
Figure 13: Inference efficiency of different pre-trained forecasting models. Left: GPU Memory
depending on the batch size. The maximum available GPU memory was 48 GB in the experiment (Nvidia A40). Right: Inference Time per sample depending the batch size.
28

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GiftEval
Agg
GittEval
TiRex
0,61
TiRex
3.1
0.44
0.64
PatchTST
6.3
TimesFM
0.63
TabPFN-TS
6.5
PatchTST
Chrones Bolt
6.7
Chronos Bolt 5
0.49
0.74
TimesFM 2.0
Chronos Balt
0.49
0.72
Chronos
0.49
0.84
Moirai
7.5
0.80
Moirai
7.5
Mcirai
0.83
TFT
8.1
Chronos
0.56
Chronos
10.2
Chronas
0.56
0.79
Chronos
0.58
1.17
TimesFM
0. 64
0.78
N-Beats
13.2
DLincar
0.66
0.96
DLinear
14.1
TTM-2
DeepAR
14.3
DeepAR
0.80
TTM-2
Auto ARIMA
0.84
00
Auto Theta
0.80 8.
15.4
Seas. Naive
1:80
Seas. Naive
16.7
0.0
0.2
0.4
0.6
0.8
1.0
1.2 1.4
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
Zero Shot
Zero-Shot Leak
Task Specific
Local
CRPS MASE
Figure 14: Results for the multivariate data subset of the GiftEval ZS benchmark: The aggregated scores and the average CRPS rank of the benchmarks' short-term sub-results are shown. Lower values are better. "Zero-shot Leak" refers to models that are partly trained on the benchmark datasets. We trained TiRex with different seeds and report the observed standard deviation of the aggregated scores.
29

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D.4 Ablations
Contiguous Patch Masking (CPM) CPM applies 2 hyperparameters: Pmnak: which defines the maximum masking probability sampled per sample, and maskk which defines the maximum for the number of consecutive patches sampled per sample. As pre-training computational demand hinders an extended hyperparameter search, we heuristically selected ( paas 0.25, which corresponds to a typical dropout probability of time series models, and mmss 5 to ensure multi-patch forecasts spanning multiple tokens. To analyze the sensitivity of the model performance to these parameters, we additionally trained TiRex variants spanning the combinations of P {0.1, 0.25, 0.5) and emas = {0, 3,3,5, 7, 9}. Figure 15 illustrates the results: The results are not very sensitive to the parameters as long as CPM is utilized (C > 0). Additionally, good long-term forecasts require sufficient training samples with multi-patch forecasts spanning multiple tokens, i.e...mask > 3 or Prmas 2 0.5 (the latter more likely leads to neighboring masked patches that effectively mask out more than Cmak patches).
Augmentations We do not apply each augmentation to every sample. Due to the computational cost of pre-training, extensive hyperparameter search not feasible. Instead, we heuristically selected application probabilities under the hypothesis that augmentations are beneficial, but excessive may lead to diminished returns. We chose an application probability of 0.5 for both Censor and Amplitude Modulation. For Spike Injection, we used lower probability of 0.05, as its computational cost higher, and frequent application creates speed bottleneck in training.
To analyze the sensitivity of TiRex's performance to these application probabilities, we trained additional variants with altered values. Specifically, tested probabilities in {0, 0.1, 0.25, 0.75, 1} for Censor and Amplitude Modulation, and probabilities in {0, 0.01, 0.3) for Spike Injection. Figure 16 summarizes the results. The analysis indicates that model performance is relatively robust to variations in application probability as long as the augmentations are utilized at all. However, targeted tuning may yield marginal improvements.
Chronos-Boo architecture trained with our data pipeline In order to isolate the impact of our dataset and augmentation pipeline from other methodological contributions, we trained Chronos- Bolt architecture, as representative of a state-of-the-a pre-trained model. Chronos- -olt was selected due to its publicly available code and configuration, though the exact training data and procedure remain undiselosed. We used the same training hyperparameters (e.g., learning rate, warmup schedule, data pipeline leads to improved performance
...)) as for TiRex. Figure 17 shows that integrating compared to the published Chronos-Bolt results on the GiftEval-ZS benchmark, while we see a mixed effect on the Chronos-ZS benchmark. Nonetheless, TiRex consistently outperforms the optimized Chronos- Bolt variant, which highlights the contributions of both CPM and the XLSTM backbone to TiRex's effectiveness. This difference is most pronounced for long-tenn term-termmee forecasts.
GiftEval-ZS Overall
GiftEval-ZS Long
GiftEval-ZS Short
0.445
0.445
0.445
0:37
0.37
0.37
0.37
9.0 7.0 5.0 3.0 1.0 0.0
0,471
0.471
0.471
max consacutive (Cro))
Tha conseeciiiiiv (Gee)
0.49
0.423
0.425
0.41
max consacutive ice
0.346
0.335
0.328
0.36
0.461
0.457
0.452
5.0 10
0,48
0.417
0.417
0.406
0.341
0.337
0.323
0.455
0.457
0.451
9.0 7.0 5.0
0.412
0.431
0.408
0.43
0.329
0.325
0.322
0.455
0.456
0.452
0.409
0.432
0.409
0.42
0.323
0.336
0.324
0.452
0.447
0.451
0.46
-0.3
0.41
0.41
0.415
0.325
0.321
0.326
0.453
0.456
0.46
-045
0.1
0.25
0.5
0.1
0.25
0.5
0.1
0.25
0.5
probality (pras)
probality (Pvod)
probalit (Praad
Figure 15: CRPS results on the GiftEval-ZS benchmark of TiRex variants trained with different set of hyperparameters for Contiguous Patch Masking (cmmux = 0 indicates that Contiguous Patch Masking not used). The parameters used for training TiRex are enclosed in red frame.
30

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Censor Augment.
Amplidude Modulation
Spike Injetion
Difference in Agg. Score
Difference in Agg. Score
-0.01
Diffrrncee AnA...
-0.02
-0.02
-0.03
-0.04
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.0
0.1
0.2
Augmention Apply Probablity
Augmention Apply Probablity
Augmention Apply Probablity
gift-eval-MASE
gift-eval-CRPS
chrenos-z5-gmean mase
chrones-E-ggmenn,
Figure 16: CRPS performance variation the EiStEval-ZS benchmark for TiRex variants trained with different augmentation application probabilities, relative baseline TiRex without augmentations. Red vertical lines indicate the parameters used in the actual model configuration.
Gift-Eval Z5 Agg Score
Gift-Eval ZS - Avg CRPS Rank
0.41
TiRex
TiRex
1.8
0.65
Chronos Bolt Base (our Data + Augmentation)
0.45
Chronos Bolt Base (our Data+Augmentatton)
0.67
Chronos Bolt Small (our Data Augmentation)
Chronos Bolt Small (our Data+ Auggeettgntttaoonn
0.68
Chronos Bolt Small (Leaderborad)
0.48
Chronos Bolt Base (Leaderboard)
0.74
Chronos Bolt (Leaderboard)
0.48
Chronos Bolt Small (Leaderborad)
3.8
0.00
0.25
0.50
0.75
2
Gift-Eval Long Term
Agg Score
Gift-Eval
Short Term
Agg Score
0.33
0.46
TiRex
TiRex
Chronos Bolt Small (our Data+ Augmeetttttt
0.41
Chronos Bolt Base (our Data=Augmentation)
0.46
0.50
0.70
Chrones Bolt Base (our Data + Augmentation)
0.42
Chronos Bolt Small (our Data+Augmentation)
0.46
0.49
0.70
Chronos Bolt Base (Leaderboard)
0.42
Chronos Bolt Small (Leaderborad)
0.49
0.55
0.75
Chronos Bolt Small (Leaderborad)
0.42
Chronos Bolt Base (Leaderboard)
0.49
0.56
0.75
0.0
0.2
0.4
0.6
0.00
0.25
0.75
Chronos ZS Agg Scores
Chronos ZS Avg WQL Rank
0.59
TiRex
TiRex
1.8
0.78
Chronos Bolt Small (our Data+ Augmentation)
0.61
Chronos Bolt Base (Leaderboard)
3.0
Chronos Bolt Base (Leaderboard)
0.62
Chronos Bolt Small aua--Augmentation)
3.1
0.80
Chronos Bolt Base (our Data=Auugmntation)
0.63
Chronos Bolt Base (our Data Augmenttgtttnnnnn
3.6
0.81
Chronos Bolt Small (Leaderborad)
0.64
Chrones Bolt Small (Leaderborad)
3.8
0.82
0.00
0.25
0.50
0.75
1.00
2
CRPS
MASE
Figure 17: Results of training Chronos-Bon Bolt architecture with the data and data augmentations as TiRex compared to the published Chronos-Boo model and TiRex. The results are from the GiftEval-P -ZZ benchmark and the Chronos-ZS benchmark.
31

---

D.5 Additional qualitative examples
In addition to Figure from the main paper, we provide further qualitative examples forecasts on the GvftEval benchmark. Specifically, Figure depicts the model behaviors for medium- and long-term forecasts and Figure 20 does same for short-term forecasts.
D.6 Finetuned -oreccd-orrennnn
To further explore the capabilitiis of our already strong pre-trained model, finetune TiRex with the training split of the GiftEval benchmark (as defined by [Aksu et al., (024). Fine-tuning is performed jointly across all training datasets. To avoid overfitting, data, using& a 20/80 ratio. For sampling, we use a uniform distribution to choose the dataset to draw the next training sample from. We freeze the input and output layers of TiRex and run over 40k steps with an initial learning rate x 10-3 and a linear learning rate decay that reaches () at the end of the run. In contrast the pre-training regime, we do not apply any data augmentation techniques (see Section 3 but still employ CPM (Section 2.1
mix the training data with our pre-training
In the finetuning setting, observe incremental improvement especially in the MASE metric (Figure 18) Specifically, we compare the pre-trained to its finetuned version well fine-tuned TTM (Ekambaram al. 2024), the only pero-shot model that provides fine-tune results on the GiftEval leaderboard.
the pre-trained model,
Gal ZS Agg Score (sorted by CRPS)
GiftEval ZS Horizion Len (Top 6) Agg Score (sorted by CRPS) Long Term
0.404 0.003
Finex-Finetuned
0.302 0.003
TiRex-Finetuned
0.415 : 0.003
0.622 0.083
0.325
0.003
TiRex
0,450
0.003
0.411 + 0.002
TTM-2 TTM-r2-Finttueed finetuned
0,400
0,482
TiRex
0.647 0.004
0.2
0.4
0.8
Short Term
0.477
TTM-r2-Finetuned
0.455 = 0.001
0.667
TiRex
0.696
0.461
0.004
0.25
0.50
0.75
1.00
1.25
TiRex-Finetuned
0.688
Zero Shot
Finetuned
Finetuned Leak
TTM-12 TTM-2-Finetuned Finetuned
0,506
0.697
CRPS
0.0
0.4
1.0
MASE
Figure 18: GiftEval-ZS benchmark evaluation results comparing the finetuned models from the GiftEval leaderboard to our pre-trained and finetuned models. We trained TiRex with different seeds, finetuned each of these models with 4 different seeds (24 seeds in total), and report the mean and the observed standard deviation of the aggregated scores.
E TiRex 1.1 Full GiftEval Zero-Shot
Subsequent to the initial release, we developed an updated model variant, denoted as TiRex 1.1, to ensure completely zero-shot evaluation on the full GiftEval benchmark. For this version, we revised the pre-training data corpus with the following modifications to eliminate any potential data leakage: (1) All datasets present in the GiftEval benchmark were removed from our training corpus, across all their respective sampling frequencies.
(2) Datasets from the Chronos-ZS benchmark that do not overlap with GiftEval were included to enhance data diversity. (3) To address a potential but difficult-to-verti might exist in Chronos training data and GiftEval despite differing frequencies we proactively removed that specific subset, thereby removing any ambiguity in its zero-shot status.
overlap in the 'solar' dataset where time series, specifically from Alabama,
Beyond the training data adjustments, we also incorporated long-period normalization, pre- processing enhancement aimed at better handling long-range periodicities. This technique addresses
32

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GinEval Full
GinEEal
GiftEval Full
Agg Score by CRPS)
Avg CRPS
Agg (sorted by CRPS)
Long Term
TiRex-1.1
0.41
0.64
TIRex-1n 1.1
3.0
0.33
Toto Base
TabPFN-TS
0.46
0.67
KingLong 300m
Toto Base 1.0
5.5
Toto Base 1.0
TiRex-1
0.35
0.47
0.49
YingLong
0.72
TabPFN-TS
7.6
Sundial Base
0.36
0.48
TimesfM 2.0
D.46
TimesFM 2.0
PatchTST
Chronos Bolt
Chronos Bolt
Sundial Base
0.47
0.49
0.49
0.67
0.74
0.72
Chronos
Chronos Bolt
Sundial Base
7.6
8.4
Ying YingLong 300m
TobPFNTS
0.37
0.38
0.52
0.53
PatchTST
0.76
Moiral L 1.1
9.1
Moirai L 1.1
0.51
Moirai B
9.2
Short Term
0.82
PatchTST
9.6
Moirai B 1.1
0.51
0.81
TFT
10.5
TRee-1.1
0.46
0.69
Chronos
0.55
0.79
12.4
TimesFM 2.0
Times
Chrenos
0.56
0.57
0.80
0.99
TimesFM 1.0
Chrones
12.4
Toto Base 1.0
0.48
0.49
0.72
N-Beats
0.71 84
DeepAR
15.4
Chronos Boft
0.74
DLinear
N-Beats
TabPFN-TS
DeepAR
1.20
ARIMA
17
Chrones Bolt
0.50
0.73
TTM r2
0.74
TTM
1
0.00
0.25
0.50
0.75
1.00
Auto ARIMA
0.96
Seas. Nalve
1:00
Auto Theta
18.5
Zero
Zero-Shot Leak
Task Specific
Auto Thela
0.98
05
Seas, Naive
20.1
Shot
Local
CRPS
0.5
10
MASE
Figure 19: Results of the full GiftEvall benchmark with TiRex 1.1: Aggregated scores of the overall benchmark and the short- and long-term performances. Additionally, the average rank in terms of CRPS, as the public leaderboard, presented. Lower values are better. "Zero-shot Leak" refers to models that are partly trained on the benchmark datasets.
the challenge of fitting long period patterns into TiRex's context window by identifying the dominant frequency of the time series and resampling it such that one period fits into context.
Figure 19 shows the performance of TiRex 1.1 on the full GiftEval benchmark alongside results from concurrent works published after our initial submission, including ToTo (Cohen et al. (002)., Sundial (Liu et al., (025)), and Yinglong (Wang al. 2025). In this updated and strictly zero-shot comparison, TiRex 1.1 maintains its state-of-the-art performance, achieving the top rank across all reported metries.
F Societal Impact
As pre-trained zero-shot model, TiRex could democratize access to modern forecasting techniques by removing the need for task-specific training or machine learning expertise, enabling broader adoption across non-expert communities. It also has the potential to enhance forecasting in data- sparse domains. Nonetheless, care must taken to ensure responsible deployment, particularly in high-stakes settings where model errors could have significant real-world consequences.
G
Code
The code repository for the model is hosted on GitHub: https://github. com/Nx -AtTXXXAAA/tteee
'GiftEval benchmark scores are reported based on the leaderboard computation at the time of our submission. A subsequent update the seasonal naive baseline affects the absolute aggregated scores but does not change any discussed model ranking, result, conclusion.
33

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et:2/15 Timeiiu
TiRex
eu2 T/medium
TiRex
5.0
1000
1500
2000
2500
2048
2287
2527
500
1000
1500
2000
25.00
2048
2287
2527
TimesFM
TS
Chronos
2048
2287
2527
2287
2527
2287
2527
2287
2527
2287
2527
2287
2527
bitbrains__mon rnd/5 T/medium
TiRex
bitbrains b mdd57/mmeilum
TiRex
1000
TimesFM 2.0
TabPEN-TS
Chronos Ball Base
TimesFM
TabPFN-TS
Chronos Ball Base
2048
2257
2527
2297
2527
2287
2527
2287
2527
2287
2527
2287
2527
bizitobs_serviceelelee wwwviiicee//////miiium
5olar/10T/medium
2048
1000
1500
2500
2048
TimesFM 2.0
TabPFN-TS
Chronos Bolt Base
TimesFM 2.0
TabPFN-TS
Chronos Bolt Base
TiRex
seapsteel//////onng
TiRex
500
1000
1500
2000
2500
2048
2287
2527
500
1000
1500
2000
2500
2048
2407
2767
TimesFM 2.0
TabPFN-TS
Chronos Bolt Base
TimesFM 2.0
TabPFN-TS
Chronos Bolt Base
2048
2287
2527
22.87
2527
2287
2527
2407
2767
2407
2767
2407
2767
Signal
Prediction (5th quanqiia
Prediction range (2nd to 8th quantile)
Figure 20: Examples medium- and long-term forecasts from the GvftEval benchmark. For each example, we show one plot with the full context and the TiRex prediction, well as zoomed-in forecasts of the best-performing zero-shot models.
34

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bidlobb servicce/OSSshort
TiRex
bizitobs servicce10SSShort
TiRex
500
1000
1500
2000
2048
2077
2107
500
1000
1500
2000
2048
2077
2107
Chronos
Chronos
2048
2077
2107
2077
2107
2077
2107
2077
21.07
2077
2107
2077
2107
bitbrains, bitbrains_md//T/// md/5T/short
TiRex
hierarchical sales/D/short
TiRex
1500
1000
TimesFM 2.0
TabPEN-TS
Chronos Ball Base
TimesFM 2.0
TabPFN-TS
Chronos Ball Base
2048
2071
2095
2071
2095
2071
2095
2062
2077
2062
2077
2062
2077
mestaurant/D/short
cavid_ deaths/DD/hortt
200
250
300
2048
50
100
200
2048
TimesFM 2.0
TabPFN-TS
Chronos Bolt Base
TimesFM 2.0
TabPFN-TS
Chronos Bolt Base
TiRex
eu2/155/short
TiRex
MMM
500
1000
1500
2000
2048
2073
2005
500
1000
1500
2000
2048
2071
2095
TimesFM 2.0
TabPFN-TS
Chronos Bolt Base
TimesFM 2.0
TabPFN-TS
Chronos Bolt Base
2048
2071
2005
2071
2005
2073
2005
2071
2095
2073
2005
2071
2095
Signal
Prediction (5th qua ouandlle)
Prediction range (2nd to 8th quantile)
Figure 21: Examples of short-term forecasts from the GiftEval benchmark. For each example, we show one plot with the full context and the TiRex prediction, well zoomed-in forecasts of the best-performing zero-shot models.
35

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Table 9: MASE scores of different zero-shot models on the GiftEval benchmark evaluation settings (Part 1/2). The models achieving the best and second-best scores are highlighted. Results for datasets that are part of the training data for the respective models are shaded in grey, and these results are excluded from the calculation of the best score. We trained TiRex with different seeds and report the observed standard deviation in the plot.
Chronns Bol B
Chronos Bok
TImesFM 2.0
TimesFM 1.0
TAPPEN-TS
Moinai L. 1.1
Moinai B 1.1
TTM-2
Chronos
Chromos
TiRex
bithrains, fast storage/STTlog
0.916 +: 0.006
0.948
0.962
0.980
32.0
1.04
0.955
0.967
1.16
1.01
1,08
bitbrains, wwsttaattragsseeeeee Ses__sttragg/SSSmmmll Umediiu
1.00
0.011
1.00
1.06
1.08
20.3
1.19
1.02
1.05
1.23
1.11
1.14
bitbrains, Los_sstoaagiSS1
0.007
0.752
bithrains, soorsstorag//l///a I/short
1.66 =: 0.013
1.07
1.08
1,09
1.18
1.15
1.09
1.18
1.28
1.11
1.14
bithrains, md/5T//ng
3.51
3.45
3.78
3.77
4.40 0.007
4,45
4.47
4.59
49.8
4.59
4.46
4.53
4.81
4.60
4.63
bithrains, md/55%/hort
1,66 0.004
1.71
1.72
1.77
1.98
1.87
1.75
1.82
2.05
1.79
1.81
Satrrans__md/Hlaee
5.84
0.011
5.88
5.99
6.09
5.96
5.93
6.07
6.16
5.79
5.89
biztoos_appllcatiee 100tttoooo//////nggg 10S/ong
3.67
0.069
10.5
9.65
4,07
16.3
7.73
7.84
13.5
9.59
9:25
9.67
bizitobs, applbictopiiiiiooo//o Dinimiiciion//SS/eeiuu
bizitohs application/ Sntpiication/OS//hurrrt
1.40
0.112
5.53
5.41
1,56
4,36
3.19
4.51
5.32
4,21
3.01
3.34
bizitobs, 12c/5T/long
1.19 0.040
1.12
1.32
1.20
bizilobs 12//5T/meccum
0.849 1. 0.028
0.878
0.920
0.887
0.870
0.987
0.853
0.992
0.942
0,880
bizitohs 12c/5T/short
0.290 +: 0.005
0.278
0.272
0.312
0.310
0.338
0.285
0.291
0.324
0.301
0.301
bizitobs_ 12c/H/long
0,590 + 0.022
0.556
0.612
1.30
1.27
1.27
1.09
1.24
1.25
1.31
bizitobs_ 12o/H/mediuum
0.525 + 0.020
0,495
0.570
1.18
1.49
0.748
1,25
1.32
1.24
1.34
1.32
bizitobs, 12b/rt
bizitohs service/10S/Img
1.57 = 0.057
5.30
4.85
2.15
7.77
3.90
4.33
6,08
5,34
4.22
3.89
bizitobs_ service/ (0S/medium
0.058
4.98
4.64
1.53
6.46
3.78
3.87
5.99
5.12
4.58
4.06
bizitobs_cd ciciibs_scrvio//ii scrvicc/10S/sbott
0,884 + 0.052
3.32
2.90
1.04
2.90
2,00
2.31
3.43
2.73
1.88
1.91
car partss//short
0,838 + 0.004
0.855
0.858
0.922
0.893
0.843
0.903
0,835
1.57
0.908
0.885
covid deaths/Dsshort
39,5 0.803
47.4
$5.6
36.5
34.6
$3.5
42.7
42.2
electricity/1511
0.891 + 0.0088
0.933
0.953
0.904
1.50
1.02
1.31
1.32
1.35
1.01
1.06
Dlectrictt//155/Tmeeel
1.
0.862
1.33
1.32
electricity/ 1S/iscr 5T//horrt
0.945 + 0.008
0.935
0.936
0.907
1.48
1.23
1.71
1,54
143
1.05
1.13
electricityDDssbor
1.43 0.010
1.45
1.48
1.49
1,75
1,49
1.51
1.50
L,66
1.56
1.60
electricity/H/ooong
1.21 0.018
1.24
1.26
1.05
1,21
1.34
1.36
1,26
1.38
1.20
1.23
electricity/H/mse
1.08 = 0.010
1.08
1.10
0.929
1.07
L.18
1.20
1.19
1,25
1.06
1.09
electricity/HHbbbott
0.009
0.951
electricity/W/bbe /W//ottt
1.46 0.010
L
1.50
1.45
1,86
1.45
1.79
1.92
2.52
1.49
1.54
et1//5//aang
1,20
1.35
ettl/1 ST/mediuu
1,04 0.009
1,06
1.11
1,08
1,27
LO0
1.30
1.24
1,14
1.32
1,36
etLl/1 /L//LST/short
0.706 + 0.007
0.680
0.704
0.719
0.875
0.787
0.925
0.825
0,812
0.801
0.872
etl////hort
1.71 0.016
1.67
1.70
1.65
1.70
1.77
1.75
1.74
1,96
1,90
1,80
ct:l ttl/H/long
1.34 0.030
L.35
1.44
1.51
1.41
1.46
1.45
1.38
1.36
1.43
1.42
LtL////mdiium
1.37
et:1/11/shor
0.827 1. 0.007
0.828
0.834
0.866
0.938
0.891
0.855
0.885
0.882
0.840
0.898
/t//Wttortt
1,73
1.54
1.66
0,932 + 0.012
0.940
0.991
0.941
1,08
0.958
1.14
1,30
0
1.14
1.11
ct22/55Tmmedium 5//meiium
eu2/15
0,910 + 0.010
0,922
0.987
0.938
1,01
0.939
1.06
1.10
0.987
1.06
1.02
e12211 ///shot
0.749 1 0.010
0.766
0.788
0.747
0.898
0.845
1.00
0,959
0.832
0.857
0.885
ett2/D/short
1,28 = 0.019
1.32
1.22
1.56
1.64
1.54
1.44
1.31
1.56
1.26
1.43
e////H//ong
1.13
et2///medium
1.05 0.021
L,03
L.05
1,05
1.12
1.28
1.18
1.03
1.10
1.15
1.14
etr2/H/short
0.742 + 0.006
0.733
0.744
0.755
0.787
0.781
0.790
ett2/W/hortt
0.797 + 0.040
0.739
0.791
1.12
1.13
0.959
1.31
0,851
1.36
0.749
0.807
hierarchical Seshs/Dshort
0.744 1 0.002
0.743
0.749
0.752
0.745
0.766
0.745
0.746
0.834
0.774
0.801
hierarchical W/shrtt
0.721 1 0.001
0.733
0.733
0.703
0.725
0.723
0.749
0.747
1.09
0.764
0.756
bospita//Mbbot
0.767 1 0.003
0.791
0.801
0.755
0.783
0.753
0.768
0,775
1.05
0.816
0.813
36

---

Table 10: MASE scores of different zero-shot models on the GiftEval benchmark evaluation settings (Part 2/2). The models achieving the best and second-best scores are highlighted. Results for datasets that are part of the training data for the respective models shaded in grey, and these results excluded from the calculation of the best score. We trained TiRex with 6 different seeds and report the observed standard deviation in the plot.
Cheonns B
Chronns Bolt
TimesPM 2.0
TimaPM 1.0
TabPEN-TS
Moirai L 1.1
Mairai B 1.1
Choonos B
Choons S
T1M-2
TiRex
jena_ weathe/ weather//UU//ong 1V1//ong
0.641 +: 0.015
0.657
0.657
0.792
mon__wather'I10 10m'medum
0.610 + 0.005
0.610
0.646
0.191
1.10
0.625
0.694
0,712
0.656
0,722
0.744
jena wwt.e//waae/////ee.e.... 10T//bort
0.297 + 0.006
0.306
0.320
0.091
0,318
0,325
0.338
0.350
0.346
0.366
0.359
1.02 1 0.014
1.05
1.03
1.20
1.23
1.14
1.15
2,53
1.12
1.14
jena weather/H/logg
0.987 +: 0.031
1.03
1.06
1.06
1.38
1.10
0.881
1,06
1.07
1.11
1.16
jena www.wwewe///ediiiiie
0.828 + 0.023
0.747
0.731
0.864
0.954
0.891
0,817
0.815
0.883
0.842
jena_ head_weathee///llee
0,516 + 0.003
0.536
0.540
0.525
0,589
0.595
0.585
0.554
0.575
0.567
0.583
kdd, sup. 2018/Drshrri
1 0.009
1.37
addd__up_2018___/ 2018//loog
0.759 + 0.027
0.684
0.925
1.03
1.09
1.06
0.867
0.960
1,00
1.14
1.24
kdl__sup__ 1aop_2018/111 8/1//meum
0,825 + 0.024
0,700
0.857
1.03
1.14
1.14
0.954
1.05
1.07
1.24
1.34
kdl. cal__cup_220 2018////hort
0.657 1: 0.006
0.601
0.667
0.941
1,09
0.894
0.944
1.01
1.04
1.06
loop_ hop_scaatle/ST//log
1.02 - 0.038
1.24
1.19
1.13
1.43
1,05
0.556
0.591
1.I1
1.31
1.38
Coop_scatlo/ST/mmll
0,941 0.019
1.12
0.972
0.450
0.523
1.07
1.11
1.61
0.572 + 0.005
0.628
0.631
0.583
0,836
0,588
0.486
0.536
0.631
0.764
0.768
loop_ prr__saatl////hhhoe
0.005
0.903
0:919
0,880
0.899
0.916
0.912
hogp_seatte/H/llng
0.917 + 0.011
0.996
1.08
0.906
1.26
0.922
1.05
1.15
1.11
1.01
1.12
0,944 1 0.012
1.02
1.10
0.934
1.32
0.948
L.00
1.14
1.19
1.05
1.14
lonp seattle/H/short
0,850 + 0.005
0.900
0.915
0.832
1.15
0.912
0.945
1,06
1.08
0.926
0.967
m4. daily/DDssortt
3.15 = 0.063
3,20
3.19
3.09
3.27
4,31
4.18
5.37
4,40
3.18
3.16
m4_ wt..borry/HHHshoee
0.719 + 0.026
0.837
0.866
0.596
0.768
0.780
m4 monthly/M/short
0.929 1 0.004
0.949
0.954
0.600
0.957
0.895
0.977
0.953
1.53
0.973
0.982
m4_qqum Htl_quarterr//OO0
0.013
0.965
2.03
m4_ weekkly///bbttt
1,90 : 0.029
2,08
2.11
2.22
2.42
2.07
2.58
2,81
3.48
2,08
2.09
m4
yeayyly////hhort
3,45 1 0.075
3.51
3.69
2.54
3.35
3.16
2.97
3.01
5.13
3.64
3.74
dense/DDshort
0.688 + 0.016
0.716
0.742
0.636
0.702
0.634
0.957
1,10
1.21
0:712
0.834
m_
densc/H/long
0.730 + 0.013
0.938
0.913
0.795
0.787
L.04
0.696
0.734
1.06
0.773
0.737
demse/t/mediumm
0.736 +
0.771
dense/ dense//Ilshott
0.788 1 0.009
0.775
0.805
0.848
0,849
0.916
0.777
0.837
1.09
0.800
0.803
resauran//D/soot
0.677 + 0.002
0.700
0.692
0.704
0.782
0.715
0.728
saugeen/Dsshot
3.12 1 0.108
2.84
2.96
3.34
3.30
3.30
3.29
2.91
4,03
3.29
2.98
sangeen/M/shn M/short
0,750 +: 0.020
0.739
0.727
0.836
0.814
0.707
0.756
0.834
0.790
0.854
0.992
saugoen/ WW/sortt
1.18 - 0.028
1.22
1.24
1,28
1,41
1.87
L.35
1.37
solar/10T/oog
0,828 + 0.021
1.07
1.19
1.15
1.58
0.915
L,95
2,02
1.10
L.66
1.98
0,879 0.037
solar/10T/horrt
1.05 + 0.032
0.991
0.947
1.48
1.49
1.08
1.11
1.10
1,18
L.11
1.22
solho/D/short
0.971 + 0.005
0.982
0.995
0.971
0,990
0.985
0.987
1,02
1,07
1.01
1.08
solau/H/long
0.697 + 0.024
1.03
0.957
1.27
1.44
0.977
1.02
1,07
1.12
L.07
1.01
solar/Hmmdduum
0.731 + 0.026
0.931
0.926
0.959
1.04
0.921
0.917
0.892
L.05
0.806
0.815
solar/H/short
0.699 0.019
0.813
0.852
0.937
0.875
0.893
0,980
0.827
0.855
Solas/W/shor
1.13 0.075
0.980
0.991
1.28
1.15
0.878
1.53
1.66
2.88
1.15
0,877
0.509 0.003
0.560
2axi//5T/medium
0.536 + 0.001
0.559
0.562
0.546
0.558
0.585
0.569
0.558
0.566
0.597
0.618
S7_ taai/a 1S/shortt
0.544 + 0.001
0.548
0.550
0.539
0.558
0.571
0.581
0,576
0.574
0.589
0.598
Laxi/H/short
0.563 + 0.002
0.562
0.567
0.560
0.566
0.582
0.601
0,588
0.597
0.576
0.579
temperature rain/Dishort
1.34 = 0.003
1,30
1.32
1.43
1.42
1.38
1.20
1.31
1.66
1.41
1.44
births/D/short
0.404 + 0.017
0.485
0.370
0.320
0.503
0.509
1.63
births/M/shhrr
0.808 1 0.066
0.924
0.756
0.497
0.622
0.588
0.771
0.723
1.32
0.778
0.572
hirohs//short
0.032
0.929
37

---

Table 11: CRPS scores of different zero-shot models on the GiftEval benchmark evaluation settings (Part 1/2). The models achieving the best and second-best scores are highlighted. Results for datasets that are part of the training data for the respective models are shaded in grey, and these results are excluded from the calculation of the best score. We trained TiRex with 6 different seeds and report the observed standard deviation in the plot.
Chaonos Boit B
Chronos Bolt
TImesF 2.0
TimexFM 1.0
TAbPEN--S
Moirai L. 1.1
Moirai B 1.1
Chronos B
TIM-2
Cheonos
TiRex
bitbrains__ase [ass_storagee/51lll
0.655 + 0.028
0.748
0.753
0.908
0.806
0.760
0.716
0,732
0,939
0.711
0.709
birbrains_ moss_sstragg/SST/T T/mediimm
0.605 + 0.016
0.755
0.867
0.881
0.746
0.735
0.636
0.662
0.906
0.804
0,803
bitbrains_ fast_ (osssstorage/SS//
0.408 + 0.005
0.454
0.435
0.447
0.476
0,412
0,413
0,596
0,463
0.446
bithrains_ fast FasLssorage/t//hss
0.699 1: 0.013
0.774
0.589
0.688
0.699
0.591
0.646
0.613
0.926
0.622
0.614
bithrains, md/55//ng
0.660 1: 0.065
0.756
0.756
0,706
0,806
0,730
0.678
0,665
1.05
1.08
birbrains_mmde mndd////////iiimm
0.594 + 0.019
0.605
0.792
0.727
0,734
0,710
0.594
0,616
0.835
0.644
0.615
bitbrains_rodd5 mroo/S//soortttt
0.403 + 0.001
0,438
0.453
0.461
0,519
0.455
0.418
0,446
0.605
0.507
0.493
Subrrains_rod//Haaoor
0,631 + 0.013
0.624
0.623
0.649
0,654
0.637
0,566
0,580
1,06
0.665
0.614
bizitobs_applliattonn 10S/ong
0.053 + 0.004
0.109
0.092
0.057
0.128
0.088
0.094
0.120
0.144
0.093
0.093
Niziooss_upplicutiii U/nm:iiimtio//SS/mddimmm
0,041 + 0.003
0.104
0.085
0,136
0,104
0.117
0.078
bizitobs hiapbiatoppliiiiioo/o i
0.013 1. 0,001
0.054
0.035
0.014
0.056
0.031
0.038
0.033
0.058
0.031
0.031
bizitobs_ 12:/5T/lon
+ 0.032
0.738
0.790
0.748
0,734
0,554
0.785
0.722
0.743
bizitohs_ 12c/5T/mediin
0.366 + 0.015
0,445
0.462
0,529
0,449
0.345
0.410
0,380
0,540
0.484
0.465
bizitobs_ 12:/5 I/short
0.078 + 0.002
0,074
0.073
0.084
0.080
0.099
0.079
0.078
0.107
0.084
0.087
bizilobs_ 12c/1//ong
0.276 1 0.010
0.278
0.295
0.728
0,724
0.440
0.600
0.495
0,751
0.738
0.780
bizitobs 12:/B/medium
0.253 1: 0.008
0.254
0.285
0.640
0.856
0.380
0.619
0.688
0.782
0.793
0.780
bizitobs_ 12//tt/borrt
0.227 +: 0.011
0.189
0.204
0.345
0.290
0.549
0.428
bizitohs Setttobs_service/OOO0 www.viceeOO//nnggggg
0.054 1. 0.002
0.113
0.096
0.062
0.137
0.091
0.104
0,115
0,140
0.094
0.093
bizitobs_ service/ /0//medium
0.034 + 0.002
0.096
0.082
0.038
0.109
0.067
0.069
0.090
0.117
0.073
0.068
bizitobs_ scrvioc//OS/isoott
0.013 + 0.000
0.051
0.032
0.015
0,051
0.031
0.032
0,042
0.053
0.027
0.027
car partts////shot
0,990 + 0.010
0.995
1.1
1,05
1,02
0.955
1.18
0.999
2.29
1.07
1.03
covid deuthi/D/chort
0.037 1 0.004
0.047
0.043
0.062
0,204
0.040
0.046
0,044
0,123
0.045
0.061
electricity/1SST 15T/long
0.075 + 0.001
0.084
0.086
0.083
0.137
0.089
0.099
0.115
0.143
0.095
0.098
Dlectiiity/1SSTTmedi
0.075 1 0.001
0,083
0.087
0.080
0.106
0.095
0.096
electricity/ 155/sso 5T//hort
0 + 0,000
0.082
0.082
0.079
0,130
0.404
0.128
0,120
0.152
0.092
0.099
electricit/D/sshor
0.056 + 0.001
0.055
0.058
0.060
0.077
0.060
0.069
0.061
0.093
0.061
0.071
electricity/HHoong
0.092 + 0.003
0.098
0.102
0.089
0.101
0.112
0.103
0.086
0,128
0.105
0.107
electricity/ Wmeeiim
0.078 1 0.002
0.081
0.084
0.073
0.082
0.091
0.087
0.082
0.109
0.087
0.088
0.061 1 0,001
0.064
0.067
0.054
0,064
0.072
0.077
0.075
0.097
0.064
0.070
electricity/WAte /Wihort
0.046 + 0.001
0.047
0.048
0.049
0.088
0.051
0.062
0.077
0.159
0.049
0.052
et1l/55//aag
0.246 1 0.003
0.298
0.296
0.358
0.352
0.400
0.450
ettl/1 5T/medium
0 + 0.002
0.281
0.288
0,278
0.329
0.248
0.342
0,324
0.333
0.379
0.390
CtLL11T/ssho
0.161 + 0.003
0.158
0.169
0.168
0.193
0.183
0.226
0.193
0.235
0.198
0.217
etlo///hort
0,282 + 0.004
0.287
0.283
0,281
0,280
0.292
0.286
0,301
0.416
0.387
0.360
et:l////oog
0.263 1 0.004
0.311
0.337
0.310
0.317
0.290
0.296
0.287
0.342
0.350
0.360
att///mmdiumm
0,253 1 0.002
0.303
0.295
0,282
0.304
0.276
0.270
0,282
0.339
0.330
0.327
etil cts//tshort
0.179 + 0.002
0.181
0.189
0.192
0.209
0.194
0.9
0.197
0.250
0.194
0.222
/tsh//thort
0.306 1 0.009
0.296
0.293
0.272
0.307
0.260
0,261
0.448
0.312
0.317
5t/2//5T/log
0.097 + 0.001
011
0.118
0,106
0,
0.101
0.115
0,137
0,126
0.134
0,9
et1211 112/15T/medium
0.093 + 0.001
0.110
0.119
0.105
0.112
0.098
0.105
0.109
0.128
0.122
0.117
e////15/short
0,066 1 0.001
0.067
0.070
0.065
0.077
0.073
0.080
0.078
0.093
0.071
0.073
etf2/D/short
0.092 1 0.001
0.094
0.091
0.108
0.113
0.129
0.094
0.095
0.119
0.092
0.097
ett2/H/long
0.116 + 0.004
1.1
0.121
0.125
0.125
0.136
0.125
0.110
0,144
0.136
022
ct2/H//cdium
0.106 + 0.002
0.115
0.118
0.110
0.126
0.128
0.118
0.100
0.139
0.132
0.136
ett2/H//hort
0.065 + 0.001
0.063
0.065
0.066
0.074
0.070
0.069
0.072
0.088
0.071
0.072
ett2/W/short
0.088 + 0.002
0.088
0.094
0.110
0,111
0.120
0.109
0,087
0,200
0.077
0.077
hierarchical hierarchicallssleeyDDDaa Dishon
0.572 + 0.002
0.576
0.582
0.576
0.573
0.593
0.580
0,575
0.792
0.600
0.619
hierarchical W/shrt
0.349 1 0.003
0.353
0.354
0.330
0.343
0.342
0.359
0.357
0,725
0.367
0.367
hospital/Mhhot
0.052 1 0.000
0.057
0.058
0.050
0.052
0.050
0.051
0.051
0.123
0.056
0.056
38

---

Table 12: CRPS scores of different zero-shot models the GiftEval benchmark evaluation settings (Part 2/2). The models achieving the best and second-best scores are highlighted. Results for datasets that are part of the training data for the respective models are shaded in grey, and these results are excluded from the calculation of the best score. We trained TiRex with 6 different seeds and report the observed standard deviation in the plot.
Cheonos Bolt B
Chronos Bolt
TimesFM 2.0
TimaPM 1.0
TabPEN-TS
Moirai L 1.I
Moirai B 1.1
Chronos B
Chonos S
T7M-2
TiRex
jena wea__wether//l weather/1U1//on 1D1/long
0.053 +: 0.001
0.064
0.063
0.035
0.069
0.055
0.077
0.070
0.068
aon__wathher'100 10m'medum
0.051 + 0.001
0.057
0.060
0.031
0.067
0.057
0.072
0.068
0.069
0.076
0.089
jena wwtpeeeaath////AAee (0b/t
0.030 + 0.001
0.033
0.037
0.016
0,036
0,035
0.051
0,053
0.455:0
0,044
0.047
0,046 1. 0.001
0.045
0.047
0.000
0.058
0.059
0.090
0.447
0.051
00000000000000000000000000000000
0.124
0.049
0.051
jena weother/H/oogg
0.057 +: 0.002
0.062
0.068
0.068
0.089
0.066
1000
0,065
0.084
0.04
0.072
jena_
0,051 + 0.002
0.084
0.058
0.066
0.065
0.000
0,058
0,057
0,073
0.070
0.069
jena_
0,041 + 0.000
0.042
0.043
0.045
0.048
0.043
0.045
0,044
0.060
0.046
0.047
kol__cup__ sup 2018/D/shorr
0.381 1: 0.005
0.372
0.373
0.378
0,380
0.359
0.381
0.376
0.452
2018//loog
0.341 + 0.014
0,300
0.419
0.518
0.537
0,462
0.378
0,418
0,542
0.624
0.712
kdl__sup_ Suup_2018/1110 8/1//mmiii
0,337 1: 0.011
0.301
0.364
0.466
0.493
0.462
0.387
0.441
0.532
0.664
0.706
kel, Baii_cup__200 2018////horr
0.270 1. 0.004
0,246
0.267
0.376
0,446
0.437
0.362
0.389
0.514
0.459
0.459
poop_scattee/S///
0.090 + 0.004
0.129
0.125
0.1
0,148
0.094
0.049
0.052
0.125
0.143
0,150
Coopsscatlo/S/mmsll
0.083 + 0.002
0.116
0.119
0.110
0.151
0.038
0,045
0.176
0,175
/ecatile//1//bor
0,049 + 0.000
0.055
0.055
0.051
0.075
0.052
0.041
0.046
0.068
0.070
0.070
loop srr_ssaatl////shhoe
0.042 0.000
0.044
0.045
0.041
0.043
0,044
0.045
0.044
0.101
0.045
hoop_seattl//Hllng
0.063 + 0.001
0.076
0.082
0.066
0.097
0,063
0.074
0,080
0.097
0,082
0.089
hrt__seattle/II/meee
0,065 1 0.001
0.076
0.082
0.067
0,100
0,065
0.070
0.080
0.104
0.084
0.088
loop_ seattle/H/short
0.059 + 0.000
0.065
0.066
0.059
0.082
0.064
0.066
0.074
0.095
0.066
0.069
m4_ daily//Dssoott
0.021 + 0.000
0.021
0.021
0.021
0.021
0.024
0.030
0.040
0.035
0.022
0.021
m4_
0.021 + 0.000
0.025
0.020
0.011
0.021
0.028
0.020
0.022
m4 monbhly/Mshhrrt
0.093 1 0.000
0.094
0.094
0.067
0,097
0.088
0.095
0.094
0.177
0.104
0.103
[44_qqurterry/QO m4_qquu
0.074 1 0.000
0.077
0.078
0.062
0.085
0.075
0.073
0.073
0.139
0.084
m4_ weeklly///bbbtt
0.035 + 0.001
0.058
0.038
0.042
0.041
0,036
0.046
0,048
0.069
0.033
0.040
m4 yearlly///hhhot
0.119 1 0.002
0.121
0.128
0.091
0.117
0.113
0.104
0.105
0.197
0.135
0.139
dense/Dishort
0.066 + 0.002
0.069
0.072
0.060
0.070
0.057
0.095
0,104
0.151
0.075
0.087
m_
densc/H/long
0.122 + 0.003
0.170
0.146
0.127
0.135
0.164
0.114
0.122
0.222
0.135
0.133
demse/t/medimm
0.121 + 0.002
0.157
0.134
0.127
0.132
0.159
0.112
0.123
denss//Tlshort
0.130 1. 0.001
0.125
0.133
0.1
0,140
0.154
0.128
0.140
0.225
0.137
0.140
resauran//D/hort
0.254 + 0.001
0.264
0.264
0,261
0,265
0.297
0.270
0.266
0.438
0.279
0.292
saugeen/Dsshot
0.382 1 0.014
0.338
0.354
0.408
0.417
0.384
0.406
0.354
0.589
0.432
0.387
sugeen/M/showe
0,303 + 0.009
0.296
0.293
0.342
0.328
0.278
0.324
0.348
0.405
0.408
0.464
sangoen/W/short /W/short
0.353 + 0.009
0.363
0.372
0.601
0.382
0.380
0.430
0.423
0.696
0.473
0.482
solar/10T/oog
0.328 + 0.008
0.443
0.497
0.498
0.703
0.352
0.771
0.903
0.545
0.748
0.901
solan/ 10T/m/Ommm
0.354 1: 0.016
D.436
0.453
0,516
0.623
0.359
0.747
0.796
solar/10T/hort
0.542 1: 0.017
0.511
0..98
0.804
0,871
0.545
0.596
0.614
0.785
0.579
0.635
solor/D/short
0.281 + 0.002
0.287
0.286
0.278
0,288
0.269
0.292
0.295
0.396
0.326
0.337
solau/H/long
0.243 + 0.008
0.405
0.373
0.493
0.572
0.324
0.347
0,360
0,512
0.464
0.441
solar/H/medium
0,260 + 0.010
0.368
0.356
0.376
0.425
0.324
0.346
0.331
0.493
0.356
0.361
solar/H/short
0,259 + 0.009
0.298
0.303
0.406
0.403
0.358
0.333
0.338
0.468
0.334
0.345
Solas/W/shor
0.154 + 0.008
0.133
0.136
0.171
0.157
0.124
0.213
0.235
0.531
0.161
0.124
sx_ Laxi/15T/lang
0.197 0.001
0.245
0.227
0,238
0.248
Laxi//ST/medium
0.202 4 0.001
0.244
0.246
0.229
0,233
0.245
0.215
0.211
0.270
0.268
0.279
S7_ taxi/ 1T/short
0.200 + 0.000
0,202
0.203
0. 0.199
0,206
0.215
0.215
0.213
0.268
0.236
0.241
Laxi/H//hort
0.136 + 0.000
0.136
0.137
0.135
0.137
0.144
0.146
0,143
0,183
0.149
0.149
temperature raih/Dishort
0,550 + 0.002
0.538
0.544
0.586
0,581
0.565
0.479
0.535
0.791
0.610
0.627
births/D/sbort
0.021 + 0.001
0.026
0.028
0.019
0.029
0.018
0.027
0.027
0.104
0.022
bisths/M/short
0.017 1 0.002
0.019
0.016
0.011
0.013
0.013
0.016
0.015
0.036
0.018
0.013
hihors//short
0.013 1 0.000
0.013
0.013
0.013
0.013
0.011
0.018
0.017
0.027
0.011
39

---

Table 13: MASE scores of TiRex compared with various task-specific and local models on the GiftEval benchmark evaluation settings (Part 1/2). Models achieving the best and second- scores highlighted, while the grey shade indicates results on datasets TiRex trained on. We trained TiRex with 6 different seeds and report the observed standard deviation in the plot.
Auto Theta
Scas Noive
DeepAR
PaleTTST
DL PLinneu
Tilex
TFI
bilbrains, fast__ Sal_ssorrgg/SS//ee
0.916 0.006
7.33
1.14
3.47
1.21
1.40
1.14
1.61
1.14
bithrains fast_ "ast__ttrage/STT sttrrage////mmdium Timedium
1.00 0.011
8.50
1,20
3.33
1.38
1.60
1.22
1,42
1.22
bitbrains Saat_storage/S//hhor
0.692 1002:::00 0.007
0.945
0.973
148
0.996
1.09
1.14
1.15
1.14
bitbrains_ H/stttt
1,66 0.013
6.06
1.34
2.65
bitbrains bibrainssrmd//11 mm//51//ong
3,35 1 0.013
4.44
3.72
6.35
3.71
3.95
3,50
4.11
3.50
bithrains mmd/5mmmddimm
7.08
bithrains bithains__nd//TTihhee /nd////shorr
1.66 - 0.004
2.10
1.98
2.63
2.27
2.18
1.97
2.07
1.77
bitbrains rnd/H/short
5.8 0.011
6.06
6,11
8.50
6.19
6.16
6.08
5.75
6.04
bizitohs, Aoplicaation/OO//long
3.67 0.069
4.47
3.19
4.25
14.8
3.83
36400
2.93
36400
cettoos_applliaationn (00////iummm/
2,85 0.057
3.22
2.77
3.88
13.8
2.57
2.69
1.78
2.69
bizitobs wwwppppppiio//lllaao USS/shett
2.24
bizitos,, 12:/5T//ong
1.19 0.040
1.32
0.686
1.12
1.06
0.968
1.45
1.24
1.45
12c/5T/madium
bizitobs_ 12c/5///h/ttttt
0,290 :::0==00 0.005
0.613
0,266
0.243
0.278
0.297
0.986
0.292
0.986
bizitobs, J2c/H/oong
0.590 0.022
0.727
0.617
0.744
0.599
0.811
1.54
1,41
4.04
bizitohs 12c/H/medium
0.525 0.020
0.737
0,537
0.676
6.63
0.701
1,56
1.65
1.65
12cbbb__2c/H/hhot
0.528 0.021
1.50
0.495
0.640
0.862
0.536
1.25
1.19
1.21
Seiiubb_eervicc//USS/aag
1.57
bizitobs Battub__serviice/1SSmmeee
1.32 1: 0.058
2.17
1.49
2,23
L68
2.59
1,32
1,06
1.12
bizitohs, Serviic///OS/shoor
2.67
1.24
1.87
2.15
1.12
hor_parts/M/sorrt
0,338 0.004
0.835
0.797
0.997
0.807
0.810
0.958
1,23
1.20
covid deattss/Dsbott
39.5 0.803
5U.7
37.7
33.2
32.9
32.8
31.4
45.4
46.9
alcctricity/1557ooee
0.891
2.28
1.24
L.03
1.15
1,50
clectricity/111//meeee 1/medium
0.841 0.006
1.39
0.977
1.31
L.1
1662
1.15
1.43
1.15
electricitt/1155//hhut
1.67
1.47
clectricit//DDshoott
1.43 + 0.010
1.89
1,85
3.56
1.86
1.85
1.82
1,88
1.99
elcetricity/H/oog
1.21 0.018
2.67
1,39
2.21
1.1
1.42
1.52
2.05
1.52
slettrcity/HH/mediumm
1.08 0.010
6.76
1.16
2.26
1.31
1.35
1.39
1,78
1.39
clectricity/IUshhort
0.869 0.009
1.23
1.08
1.31
1.29
1.44
1.36
1.74
1.36
sleetricit/W/short
2.25
2.14
2.09
eul/151/loog
1.5 + 0.009
9.34
1.00
1.19
1.34
1.42
1.19
1.76
1.19
1,20
LOS
ett an11/15 5T/shrt
0.706 0.007
1.44
0.835
0.804
LO05
0.870
0.934
0.863
0.934
cttt/D/sbort
1.71 0.016
1.69
1.68
1.98
1.86
2.04
1.85
1.75
1.78
eutl/H/log
1.34 + 0.030
2.68
1.47
1.46
1.55
1.96
1.65
2,51
1.48
ell c111/1/meeiamm
1.25 0.017
3.12
1.39
1.66
1.58
1.67
1.57
1,84
1.57
citl/H/sbort
elll/W/bort
1.72 1 0.044
4.16
1,89
2.16
1.61
1.63
1.99
1,89
1.77
etr2/157/long
1.15
ctt2/157/medium
0.910 0.010
3.27
0,933
1.21
1.10
1.09
1,05
1,04
1,05
0122/15T/sbort
0.749 0.010
4.11
0.879
0.937
1.06
1.01
1.07
0.832
1.07
elt2/D/sbort
1,28 0.019
3.64
2.17
3.25
1.31
1.54
1.45
1,85
1.39
clr2/H//ong
1.16 1: 0.037
2.49
1.43
1.58
1.45
1.26
1.28
1.46
1.13
s112///edium
1.5
2.52
ett2/11/sort
0.742 1 0.006
1.48
0.858
0.817
0.956
0.819
0.952
1,02
0.923
ctr2/W/shrtt
7.17
1.49
1,93
1.60
0.744 0.002
0.757
0.756
0.860
0.771
0.773
0.813
0.932
1.13
hierarchical sales/W/sbort
0.721 0.001
0.781
0,771
0.993
0.793
0.778
0,850
0.849
1.03
hospital//short
0.767 0.003
0.834
0,820
0.811
0.833
0.771
0.826
0.761
0.921
40

---

Table 14: MASE scores of TiRex compared with various task-specific and local models on the GiftEval benchmark evaluation settings (Part 2/2). Models achieving the best and second-bes scores are highlighted, while the grey shade indicates results on datasets TiRex trained on. We trained TiRex with 6 different seeds and report the observed standard deviation in the plot.
Auto ARIMA
Anto Theta
DeepAR
PachIST
DLibear
N-Beals
TiRex
1171
Seak
jena, weather/l0T/ong
0.641
0.0155
3.15
1.07
0.912
0.741
0,855
0,761
0.990
0.761
jona, weather/ OTT/meeiumm
Jona, jona_ [os_weather/1111 (T//short
0.297
0.006
0.574
0.552
1.96
0.450
0,527
0,743
0.368
0.743
jena Smaa_wather//Daae
1,02 0.014
1,30
1.39
1.60
1.80
1.83
1.45
1.60
1.57
0,987 0.031
6.89
1.31
1.90
1.15
1.13
1.98
2.64
1.27
jena, weather/Hmediium
0.828 0.023
1,30
1,09
0.997
0.939
0.902
1.45
1.36
0.889
Jona, weather/H/ssort
0,516 0.005
0,763
1.08
0.878
0.723
kdd cup. cup_20 18/8/Drhort
1.21 0.009
1.23
1.22
1.23
1.11
1,35
1.18
1.38
1,50
cup_ 2018//Hfong
0.027
1.11
1.18
1.18
1.37
1.34
kdd aodd_cu__201/HHH0 2018///medium
0.825 0.024
1.17
1,05
L.12
1.16
1.29
1.42
1.33
1.43
kdd sdd__up__200 2od__cu__001/111__11
0.657 0.006
1,28
1.12
L13
1.15
1,30
1.34
1.27
1.34
loop seattle/ST/lang
1.22 0.038
1.96
1,06
1.17
0.977
1.05
1,25
1.44
1,25
loop_ Poop_seattle/S//mnee seattll///Tmmmeium
0.941 = 0.019
1.27
1.05
1.12
1.1
1.05
1.15
2.06
1.15
loop_scattle/5 scattle/ST/shor
0.803
0.762
loop_seaatill seattle/Dishort
0.878 0.008
1.08
0.934
900
0.973
0.898
1.49
1.39
1.73
loop_ scattle/H/oog
0.011
0.985
0.979
1.03
0.972
0.932
2.59
2.02
1.55
loop
seattee//mmedimm
0,944 0.012
1,03
1.20
0.971
1,03
2,00
1611
1.48
loop seattle/l
0,850 0.005
0.941
1.07
1.13
1.04
1.03
1.29
1.40
1.29
dailylDKshott
3.15 0.063
4,58
3,22
3.42
3.29
3.35
3,26
3.34
3.28
m4
hourlyHH/soot
0.719 0.026
3.53
1,40
L.69
2.47
1.34
1,03
2.46
1.19
monthly/M/ssort
0.966
m4 quuatteryy/QShoor
1.18 0.013
1.44
1.32
1,46
1,30
1,21
1.28
1.19
1.60
wwwkly/W/eeeeeee W/short m4
1.90 0.029
4.62
2.34
4.64
2.68
1,97
2.36
2.66
2.78
yearly/A//hort
3.45 0.075
3.40
3.29
4.16
3,09
3.15
3,71
3.11
3.97
m, dense/D/chort
0 0.016
0.793
0.732
1.01
0.799
0.706
1.34
1.22
1.67
dense/H/lngg
0.730 0.013
0.805
0,738
0.723
1,18
1,21
2.29
1.48
m_
donsc/H/medium
0.736 0.016
0.738
0.757
0.930
0.732
0,890
1.27
L.74
1.57
dense/HU/short
1,49
restaurann/Dsshot
0.677 0.002
0.713
0.690
0.706
0.750
0.712
0.929
0.843
1.01
saugeen/D/shoe
3.12 -: 0.108
4,31
3,28
4.20
3.22
3.28
3.74
3.60
3.41
nuggen/MMshort
0.750 0.020
1.63
0.893
0.955
0.865
0.758
0.725
0.912
0.976
sange singeenWWhhort Wichort
1.18 0.028
1.31
1.55
1.81
1.55
1.54
1.55
2.12
1.99
colar/10T//on
0,828 0.021
1.28
0.912
L.18
1.00
2.03
0.871
4.53
0.871
colas/10T O'Tmmeiim
0,879 = 0.037
1.21
0.913
1,08
0.931
1.98
0.927
2.69
0.927
solar/108 WTT//rt
solar/D/shrrt
0.971 = 0.005
2.49
0.962
1.03
0.999
1,21
1.01
1.05
1.16
solar/HHoong
0.697 0.024
0,972
0.978
1.35
1.12
2,21
0.995
5.24
1.07
solar/ Dinddium
0.731 0.026
0,992
0.965
1.17
0.884
2.12
0.848
2.87
0.935
solar/H/shrtt
0.699 0.019
1.02
0.954
1.06
0.960
1.04
0.952
2.05
0.952
solar/ W//hort
1.13
2.33
T.12
s2_ 1///a/
0.509 = 0.003
0.733
U.761
0.841
0.535
0.666
0.598
0.759
0.691
xe. so.taxi//5TTmmeeiiu 1immedimm
1o__txi//1577 15Ts/ot7/hhort
0.544 0.001
0.602
0.560
0.582
0.603
0.604
0.764
0.649
0.764
se. Lisort
0.563 0.002
0.576
0.591
0.667
0.595
0.624
0.624
0.691
0.738
temperature rain/D/short
1.34 0.003
1.72
1.51
1.83
1.44
1,90
1.71
1.93
2.01
us. births/Drshort
0.404 = 0.017
0.535
0.487
0.645
0.315
0.456
1.58
1.63
1.86
births/M/shrrt
us. births/W/shhe Wihhort
1.08 0.032
1.45
1,23
1.46
1.59
1.40
1.48
1.49
1.56
41

---

Table 15: CRPS scores of TiRex compared with various task-specific and local models on the GiftEval benchmark evaluation settings (Part 1/2). Models achieving the best and second-bes beotd scores are highlighted, while the grey shade indicates results on datasets TiRex trained on. We trained TiRex with 6 different seeds and report the observed standard deviation in the plot.
Anto ARIMA
Auto Theta
Scas. Nuive
DopAR
PatchTST
DJ. Dl.incar
N-Beats
TiRes
TFT
bitbrains, fisl_storage/ST Storage/ST//ong
0.655 1: 0.028
1.01
0.669
1.33
0.734
0.791
1.29
1.36
1.29
bithrains_ fast Tos__storage/ST/eee /torage/ST/nedium
0,605 : 0.016
0.990
0.642
0.967
0.610
0.841
1,27
1,45
1.27
bitbrains_ fast_ S/sht
0.408 + 0.005
0.493
0.471
0.577
0.451
0.622
1.21
0.731
1.21
bitbrains, fast wttoatt////sssee
0.699 + 0.013
0.778
0.549
0.803
0.595
0,812
0,844
1.08
bibbrains_man md/55//long
0.660 1 0.065
0.672
0.664
1,30
0.624
1.06
1.29
1.60
1.29
bithrains, mc//5/meeium
0,594 1: 0.019
0.647
0.620
0,628
0.699
bitbrains bitbrains_md/////hll md/57/short
0,403 + 0.001
0.557
0.474
0.571
0.486
0,656
1.10
0,741
1.10
bitbrains, mud/H/shortt
0,631 + 0.013
0.585
0.603
1.07
0,650
0.715
0,874
1,38
1,30
bizitobs_ wwwpiiatiio///SAAA....
0,053 + 0.004
0.083
0.054
0.070
0.056
0.062
0.973
0.035
0.973
bizitobs_ applicationn/ Tatiicattion/O///iii 10S/medium
0,041 + 0.003
0.053
0.047
0.056
0.047
0.047
0.042
0.024
0.042
bizitobs cataubbb_ppllictiio///oo 10S/short
0.013 + 0.001
0.079
0.090
bizitobs 12c/5T/lmgg
0,581 1 0.032
0.719
0.324
0.653
0.472
0.546
0.674
0.632
0.674
bizitohs_ 12c/5T/medium
0.366 0.015
0.589
0.332
0.490
0.346
0,415
bizitobs Batnoss_2o//TT6660 12c/5T/short
0.078 + 0.002
0.179
0.074
0.080
0.077
0.100
0.262
0,080
0.262
bizitobs_ 12e/H/long
0.276 0.010
0.338
0.291
0,422
0,286
0.479
0.787
0.819
1.82
Miirobs_/c//Hmmiiin
0.253 + 0.008
0.345
0.263
0.398
0.345
0.420
0.813
0.892
1.42
bizitobs__2c/H/ibbne 12c/H/short
0.227 + 0.011
0.789
0.217
0,336
0.401
0.288
0.547
0.507
0.536
bazitobs www.eeeeeeeeiiiieeeeeeee OS/ric///////onng
0,054
0.070
0.057
0.067
0.056
0.052
Wiritohs_servic//llee Pervice//0S/mediumm
0,034 1 0.002
0.044
0.045
0,053
0.044
0.043
0.049
0.027
0.049
bizitobs_ service/ OS/shott
0.013 + 0.000
0.032
0.025
0.032
0.025
0.021
0.040
0.013
0,040
car_ pastts/M/shortt
0.990 + 0.010
0.953
1.00
1.26
0.890
1.02
1,29
1.34
1.72
covid_ covid_deaths/DDiee /estts/D//seett
0.037 + 0.004
0.177
0.067
0,063
0.037
0.071
0.030
0.095
0.125
eloctricity/1 ST//nng
0.075 + 0.001
0.155
0,081
0.129
0.084
0.123
0.129
0,401
0.129
eloctricity/15 55meeiumm
0.075 + 0.001
0.119
0,086
0.142
0.094
0.176
0.124
0.328
0.124
electricity/ ST/sbort
0,082 1 0.000
0.152
0.134
0.177
0.184
0.180
0.165
electricity/DIshort
0,056 + 0.001
0.078
0.083
0,169
0.084
0.110
0.083
0.088
0.122
(ootricity/H/llng
0.092 + 0.003
0.176
0.104
0.203
0.094
0.126
0.
0.300
0.190
electiiity/HHmmedee
0.078 + 0.002
0.454
0.081
0.206
0.091
0.115
0.156
0,254
0.156
electricity/ H//hhrr
0,061 1 0.001
0.094
0.079
0.112
0.089
0.123
0.109
0.177
0.109
clectrictt/W/shhon
0.046 + 0.001
0.092
0.095
0.111
0.107
0.123
0,100
eul/151//og
0,246 1 0.003
2.22
0.247
0,343
0,280
0.431
0.396
1.39
0.396
5T/meiumm
0,251 0.002
0.315
0,250
0.347
0.247
0.430
ettl/1 ///h//5t
0.161 + 0.003
0.320
0. 191
0.233
0.245
0.254
0.241
0.410
0.241
/tss/Dishort
0,282 + 0.004
0.293
0.304
0.376
0,330
0.387
0.279
0,341
0.515
etil/H/long
0.263 + 0.004
0.469
0.297
0.363
0.313
0.567
0,430
1.94
U.616
ettl///mediun
0,253 1 0.002
0.535
0.273
0.455
0.316
0.450
0.384
1.65
0.540
ettl/H/shert
0.179 +
0.190
0.256
0.199
0.249
etll/W/horr
0.306 1 0.009
0.686
0.323
0.447
0.406
0.372
0.305
0.319
0.358
51/2/15//llng
0.097 0.001
0.304
0.098
0.141
0.109
0.126
ett2/155T/medin
0.093 + 0.001
0.258
0.094
0.151
0.104
0.138
0,143
0,150
0.143
eu22/15/ssoort
0.066 + 0.001
0.378
0.076
0.102
0.081
0.109
0.096
0.077
0.096
ett2/D/shrt
0.092 1 0.001
0.207
0.131
0.218
0.096
0.140
0.125
0.164
0.205
ett2/H//ong
0.116 1 0.004
0.196
0.130
0.165
0.138
0.156
0.272
0.336
0.287
en1/tt/meiuum
0.106 1
0.125
0.166
0.122
0.130
ett2/1//hort
0.065 1 0.001
0.122
0.074
0.088
0.078
0.091
0.089
0.102
0.094
etr2/W/hort
0.088 + 0.002
0.728
0.142
0.194
0.160
0.294
0.1
0.160
0.169
0.572 + 0.002
0.600
0.590
0.817
0.600
0.728
0.735
0.967
2.36
Merarchical_salee/
salessW/short
0.349 + 0.003
0.379
0.358
0.582
0.382
0.439
0.485
0.474
1.03
hospital/M/short
0.052 1 0.000
0.062
0.064
0.076
0.058
0.068
0.060
0.055
0.062
42

---

Table 16: CRPS scores of TiRex compared with various task-specific and local models on the Gvl benchmark evaluation settings (Part 2/2). Models achieving the best and second-best scores highlighted, while the grey shade indicates results on datasets TiRex trained on. We trained TiRex with 6 different seeds and report the observed standard deviation in the plot.
Auto ARIMA
Anto Theta
Seak Naive
DeepAR
PacbIST
DLibear
N-Beats
TiRex
1111
jena, weather/10T/ongg
0.053
0.001
0.143
0.066
0.093
0.052
0.134
0.304
0.424
0.304
jona weather/ 0T/meeiimmm
0.001
0.073
0.065
0.098
0.052
0.089
0.277
0.350
0.277
mea__wather/1O0 (TT/short
0,030
0.001
0.063
0.064
0.129
0.069
0,104
0,155
0.130
0.155
0.046
0.001
0.062
0.053
0,073
0.069
0.193
0,080
0.082
0.297
gena wes.wweah/e//llng
0,057 0.002
0.197
0.076
0.139
0.090
0,131
0,230
1.29
0.598
jena, weather/Hmmdiiumm
0.051 0.002
0.078
0.069
0.093
0.073
0.097
0.211
0.832
0.486
Jona, weather/H/short
0,041 0.000
0.699
0,050
0.086
0.143
0.296
0.173
kdd cup_20000___ 18/8/D/hort
0.381 = 0.008
0.383
0.401
0.482
0.380
0.529
0.393
0.459
0.888
kdd cup_ 2018///long
0.341 0.014
1,09
0.477
0.583
0.503
0.660
1.05
0.970
1.25
kdd aodd_cu__011/HHHpp
2018/Hmmedi
0.337 0.011
0,442
0,442
0.548
0.472
0.660
0,851
0.791
0.949
kdd sud__cup_200 Bod__cu__208///AA.. 201///rorr
0.270 0.004
0.517
0.457
0.581
0.467
0.683
0.559
0.531
0.559
loop_ hipp_seatle//T/llg
0.090 0.004
0.184
0.095
0.131
0.088
0.117
0.137
0.231
0.137
loop_ hop_ssattee/S//mediii
0.083 0.002
0.118
0.095
0.126
0.092
0,118
0.123
0.240
0.1
loop_scattle/S1ee scattle/ST/shor
0,049 0.000
0.072
0.066
0.065
0.081
0.082
0.081
loop seattle/Dishort
0.042 0.000
0.052
0.046
0.053
0.048
0.053
0.078
0.072
0.131
loop scattle/H/oogg
0.063 0.001
0.068
0.069
0.088
0.068
0.080
0.193
0.468
0.245
Soop.seatle/HHmmedii
0,065 0.001
0,072
0,071
0.104
0.069
0,088
0,154
0.390
0.206
loop seattle/lIooonn
0.059 0.000
0.066
0.076
0.099
0.073
0.090
0.108
0.165
0.108
m4 dailylD/shott
0.021 0.000
0,030
0.023
0.029
0.023
0.029
0.023
0.024
0.026
m4 hourly/Hshoot
0.021 = 0.000
0.133
0.039
0.055
0.040
0.050
0.034
0.041
0.040
monthly/M/sbott
0.000
0.102
m4 guuatteryyyOSShhot
0.074 0.000
0.083
0.083
0.
0.083
0.096
0.082
0.079
0.099
wwwkly/ W/short m4_
0.035 0.001
0.062
0.040
0.070
0.049
0.047
0.050
0.053
0.073
m4 yeull///Short
0.119 0.002
0.113
0.117
0.168
0.110
0.134
0,130
0,115
0.138
m, dense/D/chort
0.066 1 0.002
0.076
0.070
0.123
0.077
0.087
0.135
0.126
0.294
dense/H/long
0.122 0.003
0.130
0.120
0.259
0.115
0,243
0.270
1.43
0.552
denso/H/medium m_
0.121 = 0.002
0.118
0.127
0.191
0.114
0,184
0.255
121
0.479
m_ dense/H//short
0.001
restauran//Disoot
0.254 0.001
0.270
0,262
0.340
0.284
0.342
0.362
0.329
0.907
saugeen/D/shoe
0.382 = 0.014
0,572
0,408
0.613
0.419
0.478
0.564
0.669
0.754
suggen/MM/hort
0,303 0.009
0.689
0.372
0.490
0.340
0,388
0.326
0.373
0.445
singeen/Whhort WKchort
0.353 0.009
0.397
0.484
0.673
0.491
0.574
0.549
0.734
0.855
solar/ 10T//og
0.328 0.008
0.549
0.339
0.585
0.379
1.01
0.786
6.64
0.786
Colar/10T/e O'Tmediam
0.354 = 0.016
0.485
0.356
0.552
0.362
1.00
0.771
5.67
0.771
solar/ WUT//or
0.017
1.37
2.36
0.860
solar/D/short
0.281 0.002
0.682
0,287
0.383
0.277
0,450
0.282
0.286
0.757
solar/HHoong
0.243 0.008
0.381
0,353
0.612
0.401
1.00
0.607
7.32
1.47
0,260 0.010
0.352
0.344
0.552
0,330
1.00
0.557
6.13
1.27
solar/H/shrrt
0.259 0.009
0.389
0.340
0.507
0.367
0.498
0.628
2.33
0.628
solar W/short
0.134 0.008
0.242
0.162
0.155
0.236
se_ 1///a
0.197 = 0.001
0.286
0.281
0.396
0.241
0.323
0.398
0.629
0.554
se_ wtt.////////eeeeeee 15mm/15m
0.001
0.296
0.351
So..axii/5T/shorr
0.200 0.000
0.219
0,207
0.271
0.222
0,281
0.309
0.288
0.309
sc, Lihort
0.136 0.000
0.139
0.144
0.201
0.144
0.190
0.170
0.232
0.229
temperature rain/D/short
0.550
0.002
0.682
0.644
0.830
0.592
0,840
0.694
0.761
1.63
us births/Drshort
0.021 = 0.001
0.028
0.025
0.041
0.016
0.029
0.074
0.075
0.144
births/M/short
0.017 0.002
0.016
0.017
0.017
us. W/sho
0.013
0.000
0.017
0.015
0.022
0.019
0.021
0.018
0.018
0.022
43

---

Table 17: MASE scores of different zero-shot models the Chronos-Zs benchmark datasets. The models achieving the best and second scores are highlighted. Results for datasets that are part of the training data for the respective models shaded in grey, and these results are excluded from the calculation of the best score. We trained TiRex with different seeds and report the observed standard deviation in the plot.
Chronos Bolt
TimesFP 2.0
TimestM L.D
Morai B 1.1
Chronos
RabPEN-IS
7TM-2
Chronos B
Chronos
Moiai
0.793
0.854
0.825
ETTm
0.641 = 0.006
0.633
0.621
0.620
1.04
0.806
0.755
0.826
0.781
0,803
0.718
sustralian electricity
1.06 - 0.096
0.740
0.813
1.32
0.997
0.930
1.25
1.22
1.11
1.28
0,838 1: 0.004
0,855
0.858
0.986
0.901
0.838
0.846
0.863
1.16
0,889
0.875
2016
0.923 + 0.005
0.999
1.02
0.949
1.04
0.894
1.03
1.06
1.61
0.985
0.996
covid
dominick
0.797 1: 0.004
0,856
0.871
0.935
1.13
0,864
0.830
0.828
1.31
0.824
0.812
eront
0.630 0.040
0.693
0.756
0.589
0.568
0.569
exchange rate
2.20 0.157
1.71
1.77
1.98
3.34
1.44
1.74
1.81
2.01
2,18
1.78
fred md
0.451 = 0.023
0.646
0.612
0.498
0.650
0,530
0.564
0.572
0.698
0.445
0.445
hospital
0.767 1. 0.003
0.791
0,801
0.755
0,783
0,686
0.830
0.820
0,843
0,812
0.815
ml monthly
1.05 + 0.008
1.10
1.13
1.05
1.07
1.04
1.14
1.14
1.47
1.12
1.16
quarterly
ml yearly
3.67 + 0.095
4.40
5.10
3.60
4,00
3.59
3.52
3.61
5.78
4.48
4.90
m3 moothly
0.847 = 0.009
0.851
0.869
0.832
0.935
0.845
0.902
1,23
m3 quarterly
1.17 = 0.011
1.29
1.33
1.20
1.15
1.10
1.12
1.15
1.72
1,18
1.29
m3 yearly
2.76 0.070
2.91
3.41
2.82
2.70
2.73
2.75
2.73
3.87
3.17
3.42
m4 quarterly
118 0.013
1.22
1,25
0.965
1.40
1.17
1.17
1,81
1,24
1.25
m4 yearly
3.46 + 0.076
3,51
3.69
2.55
3.37
3.18
3 ..04
3.07
4,89
3.69
3.80
nn5
0.563 = 0.007
0,576
0.583
0.608
0.629
0.665
O 586
0.638
0.998
0.594
0.618
and weekly
0.010
0.916
0.927
0.865
0.949
0.882
0.979
0.939
0.994
0,941
0.946
tourism monthly
1.47 + 0.014
1.53
1.61
1.62
1.46
1.65
1.75
3.21
1.84
1,93
tourisan quarterly
1.64 0.026
1.76
1.84
1.80
2.06
1.59
1.82
1.92
3.77
1.81
1.77
tourism yearly
3.50 -: 0.100
3.69
3.49
3.02
3.21
3.15
3.56
3,84
3.98
traffic
0.799 = 0.013
0.784
1.860
0.726
0.64
0.791
0.758
0.768
0.835
0.812
0.831
weather
44

---

Table 18: WQL scores of different zero-shot models the Chronos-ZS benehmark datasets. The models achieving the best and second best scores are highlighted. Results for datasets that are part of the training data for the respective models shaded in grey, and these results are excluded from the calculation of the best score. We trained TiRex with different seeds and report the observed standard deviation in the plot.
Chronos Holt
TimesPM 2.0
TimestM L.D
Morai B 1.1
TabPEN--S
Chronos B
Chronos S
Chronos
7TM-2
Moiai
0.079
0.085
0.082
ETTm
0.054 = 0.001
0.052
0.051
0.052
0.084
0.077
0.070
0.076
0.076
0,070
0.063
sustralian electricity
0.059 0.005
0.036
0.042
0.067
0.089
0,940
0.038
0.054
0,074
0,067
0.072
2016
0.012 + 0.002
0.990 1: 0.010
0.016
0.995
0.016
1.01
0.053
1.65
0053
0.020
0.009
0.990
0.015
0016
00038
1.38
0.012
1,07
0.012
1.03
covid deaths
0.047
0.043
0.215
0.204
0,040
dominick
0 1 0.001
0.345
0.348
0.371
0.412
0.335
0.344
0.343
0.552
0.331
0.336
eront
0.019 0.002
0.021
0.026
0.021
0.021
0.020
0.017
0,118
0.044
exchange rate
0.013 = 0.002
0.012
0.011
0.015
0.013
0.010
0.011
0.011
0.377
0.012
0.012
fred md
0.023 + 0.006
0.042
0.037
0.027
0.036
0.055
0.042
0.050
0.050
0.020
0.015
hospital
0.052 1. 0.000
0,057
0,058
0.050
0.052
0.063
0.059
0.058
0.079
0.056
0.057
ml monthly
0.136 + 0.004
0.139
0.134
0.130
0.123
0.150
0.177
0. 0.9
0.215
0.131
0.138
quarterly
0,090
ml yearly
0.135 + 0.008
0,151
0.157
1.5
0.163
0.118
0.127
0.123
0,246
0.198
0.183
m3 moothly
0.091 = 0.000
0.093
0.094
0.089
0.098
0.090
0.101
0.153
0.096
m3 quarterly
0.070 = 0.000
0.076
0.077
0.075
0.072
0.067
0.070
0.070
0.115
0.074
0.080
m3 yearly
0.131 + 0.004
0.129
D.155
0.144
0.123
0.130
0.130
0.131
0.191
0.149
0.157
m4 quarteryy
0.074 0.000
0.077
0.078
0.062
0.085
0.075
0.076
0.076
0.125
0.083
0.083
m4 yearly
0.119 = 0.002
0.121
0.128
0.091
0.117
0.114
0. 108
0. 109
0. 192
0.135
0.138
0.551 0.001
0.562
D.567
0.557
0.565
on5
0.146 = 0.002
0,0
0.151
055
060
0.173
0.152
165
0.311
0.162
0.169
and weekly
0.083 = 0.001
0.084
0.085
0.079
0.086
0.081
0.091
0.089
0.113
0.089
tourism monthly
0.077 = 0.002
0.090
0.094
0.085
0.101
0.084
0.098
0.099
0,283
0,101
0.108
tourisan quarterly
0.061 1 0.002
0.065
0.067
0.070
0.085
0.093
0.067
0.070
0.200
0.077
0.070
tourism yearly
0.148 0.006
0,166
0.168
0.163
0.148
0.148
0.137
0.138
0.212
0.199
0.201
traffic
0.235 = 0.004
0.231
0.252
0.212
0.185
0.229
0.236
0.238
5.54
0.255
0.258
weather
0.000
0.150
0.132
45

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Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer:[ Yes]
The key contributions stated in the abstract and introduction are well supported by the content of the paper. Specifically, our proposed model, TiRex, is rigorously evaluated two comprehensive benchmarks to the best of our knowledge the most extensive to date. Across both benchmarks, TiRex consistently outperforms all existing pre-trained models on both short- and long-term forecasting tasks (Figure 5 App: Figure 8 [TI. We note that most benchmark results of the compared models are not generated by us but are sourced from public lcaderboard, with most results contributed by the original model authors. However, we additionally replicated a subset of these results for verification. Furthermore, the effectiveness of each component of TiRex is validated through detailed ablation studies (Table [ App: Figure 17). highlighting the contributions of TiRex architecture, CPM and the proposed augmentation strategies.
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Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
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7. Experiment statistical significance
Question:
Does the paper report error bars suitably and correctly defined, or other appropriate
information about the statistical significance of the experiments?
Answer: [Yes]
Justification: We train TiRex using different random seeds and report the mean and standard deviation of the resulting performance metrics. our ablation studies (Table we explicitly highlight cases where the performance degradation exceeds three times the observed standard deviation across seeds, indicating statistical significance. For baseline models, whose results are obtained from a public leaderboard or rely on pre-trained models with deterministic inference, error bars are not available.
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52


Reviews:
[{"review_id": "zjz0GmbFVY", "reviewer": "Reviewer_z91z", "summary": "The paper proposes a novel LSTM based architecture for pre-trained time-series models that leveraged the xLSTM architecture. The model shows that it can perform well on zero-shot and few-shot forecasting tasks with much lower size, and efficient inference compared to other founadational time-series models", "questions": "1. Can the model be used for other tasks like imputation, anomaly detection and classification?\n2. How does the performance vary with horizon length and frequency of time-series?\n3. Can the hidden states be interpreted to model different dependencies and explanations similar to attention modules?", "limitations": "1. See Weaknesses\n2. The model can only do forecasting and not other time-series analysis tasks like imputation, anomaly detection and classification\n3. It is not as interpretable as some simpler statistical models", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 4, "originality": 2, "strengths_and_weaknesses": "## Strengths\n1. The improvement in performance given the efficiency of the model is very significant.\n2. The architecture is quite novel for time-series models. \n3. The evaluation is well done with comparison with state-of-art foundational models and benchmark suites\n4. The performance improvement is very significant shocasing that innovations in model backbone is important for founfational time-series models.\n5. Ablations on data augmentation, patching are very useful for practioners\n\n## Weaknesses\n1. It is a improvement over the xLSTM architecture with additional novelty only in input patching and simple data augmentation", "was_revised": true, "final_justification": "The authors have provided acceptable answers to all the questions. The work is very innovative with the ability to provide sota generalizable performance with low parameter recurrent models across domains. Therefore, I recommend accept.", "rebuttal": "We thank the reviewer for their feedback and for highlighting the **significance of TiRex's performance improvements, its architectural novelty, the thoroughness of the evaluation, and the practical utility of the ablation studies.**\nIn the following, we address the reviewer's views on weaknesses and answer the questions by the reviewer, point by point:\n\n> 1. It is a improvement over the xLSTM architecture with additional novelty only in input patching and simple data augmentation\n\nWhile the xLSTM backbone is indeed a foundational element we would like to clarify our contributions, as our work introduces two other key contributions that are crucial for achieving the final performance.\n- **Contiguous Patch Masking (CPM):**  CPM combined with our “masked inference “mechanism addresses the challenge of autoregressive error accumulation in long-horizon forecasting, enabling stable and coherent predictions where previous models fail. This is in contrast to a naive multi-patch training approach, which we show harms short-term performance, and standard autoregressive inference, which degrades long-term performance (Table 1).\n- **Data Augmentations:** The proposed online augmentations demonstrate their importance in improving the model's robustness and generalization capabilities (Table 1).\n\nThe synergistic combination of the xLSTM architecture, the CPM training strategy, and our specialized data augmentations, which together establish the TiRex model, therefore represent our main contributions.\n\n> 1. Can the model be used for other tasks like imputation, anomaly detection and classification?\n\nWhile we did not analyze these tasks in the paper, we believe the model holds significant potential for them. Similar to how pre-trained models in other domains provide powerful feature extractors, the hidden representations of TiRex could be leveraged for various downstream tasks. The state-tracking capability of the sLSTM modules, in particular, may provide a rich, compressed representation of the time series dynamics, suitable for tasks like anomaly detection or classification. We will add this discussion to our future work section.\n\n> 2. How does the performance vary with horizon length and frequency of time-series?\n\nOur evaluation shows that TiRex excels across various horizon lengths and frequencies.\n- **Horizon Length:** Figures 9, 10, and 11 in the appendix provide a detailed performance breakdown on the GiftEval-ZS benchmark for long-term (600-900 steps), medium-term (100-600 steps), and short-term (< 100 steps) forecasts, respectively. TiRex achieves the top rank in all three categories, with its most significant performance gains observed in long- and medium-term forecasting.\n- **Frequency:** The GiftEval and Chronos-ZS benchmarks were chosen specifically for their diversity, hence also covering different frequencies (as detailed in Tables 7 and 8). TiRex's number one overall rank on both benchmarks (Fig 4 and 5) demonstrates its strong and robust performance across these different time scales. For GiftEval TiRex is the top-performing model for daily, hourly, minutely, and secondly datasets, and among the top three for weekly, monthly, and quarterly datasets.\n\n> 3. Can the hidden states be interpreted to model different dependencies and explanations similar to attention modules?\n\nWhile a detailed interpretability study was beyond the scope of this work, the architecture of TiRex is promising for such analysis. Unlike transformer models, which rely on attention maps for interpretation, TiRex utilizes sLSTM modules with explicit recurrent state vectors. We hypothesize that this state vector acts as a compressed summary of the time series history. Analyzing these state dynamics could offer a powerful and potentially more direct way to understand the model's forecasting strategy, in future research."}, {"review_id": "Y7TLheV60C", "reviewer": "Reviewer_ru3x", "summary": "There has been lots of recent work on zero-shot time series forecasting with pre-trained time series foundation models. Most of these models are based on transformers, which often struggle with time-series data. On the other hand LSTM are excellent at state-tracking, making them a classic choice for time-series, but they traditionally lack the strong in-context learning abilities of Transformers. This paper aims to bridge this gap. The authors introduce TiRex, a new zero-shot forecasting model that has the state-tracking strengths of LSTMs and the powerful in-context learning ability. The model is built on xLSTM, an enhanced LSTM with strong in-context learning ability. To help address the quantile collapsing problem, the model used contiguous patch masking (CPM) to random mask consecutive patches during training. Multiple training data augmentation methods are proposed to improve the model’s prediction ability. The model achieves state-of-the-art results, outperforms other foundation models such as TimsFM, Chronos, Moirai.", "questions": "No", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 4, "originality": 4, "strengths_and_weaknesses": "The paper leveraged new model structure (xLSTM), new training method (CPM) and better data augmentation specifically censor augmentation, amplitude modulation and spike injection to improve state-of-the-art results by a significant amount (Figure 4). Among the three points, I believe 1, 2 are new and the specific data augmentation method is also new although I could be missing something here. In terms of the impact, I think CPM is the most impactful for two reasons 1) addressing collapsing quantiles problems in other models such as Chronos Bolt and Times FM. 2) looking at Table 1, not using CPM seems to lead to the most performance loss.", "was_revised": true, "final_justification": "The was no discussion during rebuttal and I will maintain my recommendation of  Accept.", "rebuttal": "We thank the reviewer for their careful summary of our work. We are glad they recognized the novelty of leveraging the xLSTM architecture and our proposed Contiguous Patch Masking (CPM) training strategy. We especially appreciate that the reviewer highlighted the impact of CPM in addressing the collapsing quantiles problem and its significant contribution to the model's overall performance."}, {"review_id": "lT2u3D6erW", "reviewer": "Reviewer_yiaE", "summary": "This paper leverages the recently introduced xLSTM architecture to build a time-series foundation model and shows that it outperforms competing models in terms of both efficiency and forecast accuracy.", "questions": "1. The authors showed that TiRex can predict periodic spikes well, which is a common failure mode for other time-series foundation models. This is not surprising given the specific data augmentation techniques (e.g., spike injection) employed to train TiRex. But how well can TiRex generalize to situations not well covered in the training data. For example, what will TiRex predict when faced with aperiodic spike trains (e.g., from neuroscience)? It would be interesting to test TiRex on synthetic time series where different aspects of the signal can be controlled.\n2. What are some failure modes of TiRex that the authors have observed? Understanding these failure modes will help further improve the model.\n3. Did the authors find any interpretable strategies TiRex is using to make zero-shot forecasts?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**:\n1. The experiments are well designed, well thought out, and extensive, which lends credibility to the results.\n2. The improvements over existing zero-shot models (Chronos, TimesFM, etc.) are quite substantial, and the underlying architecture of TiRex is quite different from transformer-based models, which will help move the field forward.\n3. The paper is well written.\n\n**Weaknesses**:\n1. There is very little theoretical analysis, it is not clear on a fundamental level why TiRex does better than other models, and what its potential failure modes are.", "was_revised": true, "final_justification": "I appreciate authors' response, especially concerning the potential theoretical advantages of TiRex. I wish the authors included new data for some of my other questions, but this does not change the fact that this is a very good paper with potentially significant contribution to the field of time series foundation models.", "rebuttal": "We thank the reviewer for their feedback and for **positively highlighting the experimental design, the substantial performance improvements, the novelty of the architecture, and the quality of the writing.**\nIn the following, we address the reviewer's views on weaknesses and answer the questions by the reviewer, point by point:\n\n> 1. There is very little theoretical analysis, it is not clear on a fundamental level why TiRex does better than other models, and what its potential failure modes are.\n\nWe appreciate the reviewer's desire for a deeper theoretical understanding. While our paper focuses on the construction of the approach and its empirical validation with the respective ablations, we believe one can ground TiRex's superior performance at least partly in the established theoretical properties of its backbone: As shown by [1,2,3], recurrent architectures like sLSTMs occupy a higher class of formal languages than transformers. Specifically, their state-tracking ability allows them to solve problems (e.g., parity, counting) that are provably beyond the reach of standard transformers (Figure 7). We hypothesize that this fundamental expressivity advantage allows TiRex to better model temporal dynamics, leading to better performance, especially across long horizons. We alluded to this aspect in the appendix, but the reviewer comment shows that we did not link this well enough. Hence, we will clarify this connection in the final version.\nRegarding failure modes, we address this in the second next point.\n\n> 1. The authors showed that TiRex can predict periodic spikes well, which is a common failure mode for other time-series foundation models. This is not surprising given the specific data augmentation techniques (e.g., spike injection) employed to train TiRex. But how well can TiRex generalize to situations not well covered in the training data. For example, what will TiRex predict when faced with aperiodic spike trains (e.g., from neuroscience)? It would be interesting to test TiRex on synthetic time series where different aspects of the signal can be controlled.\n\nWhile our spike injection augmentation was indeed key, we designed it specifically to encourage generalization rather than memorization:\n1) **Diverse Spike Features:** The augmentation is more complex than simply adding a repeating spike. As detailed in Section 3 and Appendix B, we introduce significant diversity by randomizing:\n- **Spike Shape:** We use multiple kernels (Tophat, RBF, Linear) to define the spike's shape.\n- **Spike Parameters:** The width and amplitude of each spike are sampled from distributions.\n- **Temporal Structure:** The periodicity itself is randomized for each sample, and we use a variety of underlying temporal patterns.\nThe goal of this diverse training is to teach the model a general concept of \"sharp, transient events\"  and understand them “in-context”, rather than having it memorize a simple periodic pattern.\n\nWe will extend the explanations in the main paper (Section 3) and Appendix B to make this more clear.\n\n2) **Predictability of Aperiodic Spikes:** A truly stochastic spike, with no causal link to the preceding signal, is by definition unpredictable from the context alone. In this case TiRex might provide an estimation of the expectation with high uncertainties. However, if spikes are triggered by the system's underlying dynamics, we hypothesize TiRex would be uniquely suited to generalize as the sLSTM's state-tracking, might allow to model the latent state leading up to an event - a potential advantage over architectures that may be limited to pattern matching.\n\n\n> 2. What are some failure modes of TiRex that the authors have observed? Understanding these failure modes will help further improve the model.\n\nWhile we did not observe any specific repetitive failure modes in the evaluation, two hypothetical ones are worth noting:\n- As discussed in the limitations section, our current model treats multivariate time series as a collection of univariate ones. While this approach is strong, as reflected in the Gift-Eval results (8 out of 23 datasets are multivariate) and pointed out in previous work [4] it may fail in scenarios where forecasting is impossible without explicitly modeling interdependencies between variates.\n- As a zero-shot, in-context learning model, TiRex's performance depends on having a sufficient context of past values to identify the time series' properties. When faced with a very short context that does not exhibit the characteristic patterns of the series, its forecasts may be unsatisfactory, a natural limitation of this paradigm.\n\n> 3. Did the authors find any interpretable strategies TiRex is using to make zero-shot forecasts?\n\nWe did not find any specific interpretable strategies. However, we also did not explicitly search for them. It is likely that for specific forms of time series TiRex would use straightforward strategies to construct its forecast.\n\n**References**\n\n[1] Beck, M., Pöppel, K., Spanring, M., Auer, A., Prudnikova, O., Kopp, M. K., Klambauer, G., Brandstetter, J., and Hochreiter, S. xLSTM: Extended Long Short-Term Memory. NeurIPS 2024.\n\n[2] Merrill, W. and Sabharwal, A. The parallelism tradeoff: Limitations of log-precision transformers. TACL 2023\n\n[3] Delétang, G., Ruoss, A., Grau-Moya, J., Genewein, T., Wenliang, L. K., Catt, E., Cundy, C., Hutter, M., Legg, S., Veness, J., and Ortega, P. A. Neural networks and the Chomsky hierarchy. ICLR 2023.\n\n[4] Nie, Y., Nguyen, N. H., Sinthong, P., and Kalagnanam, J. A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. ICLR 2022."}, {"review_id": "492waHgtRh", "reviewer": "Reviewer_Hidj", "summary": "This paper introduces TiRex, a pre-trained time series forecasting model leveraging xLSTM, a modern LSTM variant, to address the limitations of existing zero-shot forecasting approaches. TiRex integrates Contiguous Patch Masking (CPM), a novel training-time masking strategy, and three data augmentation techniques to enhance state-tracking and generalization. Experiments on HuggingFace benchmarks GiftEval and Chronos-ZS demonstrate that TiRex outperforms significantly larger models (e.g., TabPFN-TS, Chronos Bolt) in both short- and long-term forecasting, with fewer parameters (35M) and faster inference speed. The model’s success stems from combining xLSTM’s in-context learning with CPM to mitigate autoregressive error accumulation and augmentations to handle diverse time series patterns.", "questions": "Please make responses to these weaknesses.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths** \n\n1. By integrating xLSTM, TiRex bridges the gap between LSTM's state-tracking and transformer's in-context learning, enabling robust long-horizon forecasting.\n\n2. CPM enhances multi-patch prediction stability, while augmentations (amplitude modulation, censor augmentation, spike injection) improve generalization to rare patterns.\n\n3. Sets new SOTA on zero-shot benchmarks, outperforming larger models with 11× faster inference than TimesFM-2.0.\n\n**Weaknesses**\n\n1. Currently focuses on univariate time series analysis, with multivariate modeling explicitly noted as a direction for future research.\n\n2. Omits evaluation on widely adopted benchmark datasets (e.g., ETTH1, ETTH2, ETTM1, ETTM2, Weather, Electricity) that are routinely used in state-of-the-art (SOTA) studies [1]. This gap limits direct comparability with prior works and may obscure the model's generalizability across diverse time series modalities.\n\n3. Lacks publicly available codebase for independent verification, which hinders reproducibility and community validation of the reported findings.\n\n[1] Woo, G., Liu, C., Kumar, A., Xiong, C., Savarese, S., & Sahoo, D. (2024). Unified Training of Universal Time Series Forecasting Transformers. In Proceedings of the Forty-First International Conference on Machine Learning.", "was_revised": true, "final_justification": "Since most experimental results on datasets are included in this research, and most concerns are addressed by authors,  I would like to raise the score.", "rebuttal": "We thank the reviewer for their thorough summary and for acknowledging the strengths of our work, including the **novel integration of xLSTM, the benefits of CPM, and the model's state-of-the-art performance and efficiency.**\nIn the following, we address the reviewer's views on weakness as requested in the questions by the reviewer:\n\n> 1.Currently focuses on univariate time series analysis, with multivariate modeling explicitly noted as a direction for future research.\n\nThe reviewer is correct that TiRex models each time series variate independently. We identified this as a limitation and an area for future work. However, we want to emphasize that this approach remains remarkably effective. Previous work (e.g., [1]) has shown that univariate models can be strong on multivariate tasks.\n\nOur results on the GiftEval benchmark, which includes multiple multivariate datasets (8 out of 23), confirm this. TiRex outperforms models designed specifically for multivariate forecasting (e.g., Moirai, TTM) on the overall benchmark (Figure 1). To make this point more explicit, **the table below shows the performance (Top 3 models by CRPS) on just the multivariate datasets within the GiftEval-ZS benchmark, where TiRex still achieves the top rank**. This demonstrates that for many real-world problems, accurately modeling individual series dynamics is the most critical factor. \n\n|Model | CRPS | MASE |\n| --- | --- | --- |\n|TiRex | 0.40 | 0.61 |\n|TabPFN-TS | 0.44 | 0.64 |\n|TimesFM 2.0 | 0.45 | 0.63 |\n\nWe will add this extended discussion to the paper.\n\n> 2. Omits evaluation on widely adopted benchmark datasets (e.g., ETTH1, ETTH2, ETTM1, ETTM2, Weather, Electricity) that are routinely used in state-of-the-art (SOTA) studies. This gap limits direct comparability with prior works and may obscure the model's generalizability across diverse time series modalities.\n\nWe note that **our evaluation already includes all the datasets the reviewer is concerned about.** As detailed in our appendix, the GiftEval benchmark includes ETTh1, ETTh2, ETTm1, ETTm2, and Electricity. The Chronos-ZS benchmark includes the Weather dataset. The individual results are presented in Tables 9 to 18 in the appendix.\n\nOur choice to use the GiftEval and Chronos-ZS benchmarks instead of the older LFS-benchmark (which consists of the datasets mentioned) was deliberate and made to ensure a more rigorous, transparent, and comprehensive evaluation. We will explain this in the final manuscript. \n\nIn short, recent work [e.g., 2,3] has criticized the LFS benchmark for issues with inconsistent evaluation protocols and limited diversity, which hinder generalizable comparison. In contrast, GiftEval and Chronos-ZS offer:\n\n1) **Greater Diversity and Generalizability:** GiftEval contains 97 evaluation settings across 23 diverse datasets, while Chronos-ZS contains 27 datasets --- both covering diverse domains. This provides a much broader test of a model's zero-shot capabilities than the 6 datasets in the LFS benchmark.\n2) **Standardization and Reproducibility:** Both benchmarks are hosted on public leaderboards with standardized evaluation code, ensuring that all models are compared fairly under the same conditions. This resolves comparability issues present in prior work.\n\nTherefore, by using these comprehensive benchmarks, we are confident that our evaluation provides a more robust and comparable assessment of SOTA performance across a wide range of time series domains.\n\n> 3. Lacks a publicly available codebase for independent verification, which hinders reproducibility and community validation of the reported findings.\n\nWe fully agree with the reviewer on the importance of reproducible evaluation results. We will release our model, the respective code, and the evaluation scripts to allow for the full verification of our benchmark results. The reproducibility of our findings will be also ensured by our submissions to the public GiftEval and Chronos-ZS leaderboards, which require the necessary code and model to validate the results.\n\n---\n\nWe thank the reviewer for the opportunity to address their feedback. Given that we have now addressed primary concerns --- e.g, the evaluation results for the noted datasets and committing to a public release of our model --- we hope the reviewer will consider adjusting the initial score accordingly.\n\n**References**\n\n[1] Nie, Y., Nguyen, N. H., Sinthong, P., and Kalagnanam, J. A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. ICLR 2022.\n\n[2] Bergmeir, C. Fundamental limitations of foundational forecasting models: The need for multimodality and rigorous evaluation, Time Series in the Age of Large Models Workshop NeurIPS 2024\n\n[3] Aksu, T., Woo, G., Liu, J., Liu, X., Liu, C., Savarese, S., Xiong, C., and Sahoo, D. GIFT-eval: A benchmark for general time series forecasting model evaluation. In NeurIPS Workshop on Time Series in the Age of Large Models, 2024."}]

Author rebuttal:

Meta-review: The paper introduces TiRex, a zero-shot time-series forecasting foundation model that builds on xLSTM and adds two key ingredients: Contiguous Patch Masking (CPM) and a set of online data augmentations (censor augmentation, amplitude modulation, spike injection). The central claims are:

- TiRex (∼35M params) achieves SOTA zero-shot performance on GiftEval-ZS and Chronos-ZS, outperforming substantially larger baselines (e.g., TimesFM, Chronos/Bolt, Moirai) while offering faster inference.

- CPM + masked inference mitigate autoregressive error accumulation / quantile collapse, improving medium/long-horizon forecasts.

- Strong results across horizons and frequencies and univariate modeling still excels on several multivariate datasets within GiftEval.

- Removing CPM produces the largest degradation while augmentations and patching also matter.

Strengths:

- Improvements are consistent and sizable across two rigorous, standardized benchmarks.

- CPM is simple and effective and ablations isolate its contribution to stabilizing multi-patch prediction and combating quantile collapse.

- Horizon-specific and frequency-specific analyses are useful ablations for practitioners.

- Smaller model + faster inference are valuable for deployment.

- The paper is well written and the problem framing and design choices are easy to follow.

Weaknesses:

- Advances largely combine a new backbone (xLSTM) with CPM and simple augmentations. While the empirical contribution is strong, the methodological novelty is incremental beyond xLSTM.

- The paper lacks formal analyses for why CPM + xLSTM reduce quantile collapse or improve long-horizon stability.

- No systematic interpretability study (e.g., state dynamics inspection) to illuminate failure modes or decision rationales.

- The spike results are compelling, but stress testing on aperiodic/synthetic spikes would strengthen generalization claims.

- Focuses on univariate modeling while broader multi-variate modeling is deferred.

Primary reasons:

- Strong, consistent empirical gains over established zero-shot foundation models on standardized, diverse benchmarks, using a compact recurrent architecture with clear speed advantages.

- Practical, reproducible training ideas that others can adopt.

These outweigh the concerns about limited theoretical analysis and incremental novelty beyond xLSTM. However, given those concerns, I recommend Poster. The paper stands out by demonstrating that carefully trained recurrent backbones can outperform much larger transformer-based TFM baselines in zero-shot forecasting, with an ablation-supported training mechanism that appears broadly useful.

Discussions:

- z91z (final: Accept/5):
Praised efficiency and performance; initially questioned whether novelty beyond xLSTM reduces to patching + simple augmentations. After rebuttal, maintained Accept.

- ru3x (final: Accept/5):
Viewed CPM as the most impactful element. Minor discussion; kept Accept.

- yiaE (final: Accept/5):
Asked for theory, unseen-pattern generalization (aperiodic spikes), and failure modes/interpretability. Authors pointed to recurrent expressivity results and diversity of spike augmentation. No new data added, but the reviewer still found the paper very good and kept Accept.

- Hidj (final: Weak Accept/raised score):
Requested theoretical guarantees and noted missing classic datasets; authors clarified those datasets are included via GiftEval/Chronos-ZS and committed to code release. Reviewer increased score to Weak Accept.

Weighing: Three Accepts and one Weak Accept after rebuttal. The novelty and theory reservations remain, but the empirical strength, ablation evidence, efficiency gains, and clarity justify acceptance.
Decision: Accept (poster)