LightGTS: A Lightweight General Time Series Forecasting Model
Authors: Yihang Wang
Yuying Qiu
Peng Chen
Yang Shu
Zhongwen Rao
Lujia Pan
Bin Yang
Chenjuan Guo
Venue: ICML 2025 poster (2025)
Keywords: Foundation models; Time series forecasting
Primary area: deep_learning->sequential_models_time_series

Abstract: Existing works on general time series forecasting build foundation models with heavy model parameters through large-scale multi-source pretraining. These models achieve superior generalization ability across various datasets at the cost of significant computational burdens and limitations in resource-constrained scenarios. This paper introduces LightGTS, a lightweight general time series forecasting model designed from the perspective of consistent periodical modeling. To handle diverse scales and intrinsic periods in multi-source pre-training, we introduce Periodical Tokenization, which extracts consistent periodic patterns across different datasets with varying scales. To better utilize the periodicity in the decoding process, we further introduce Periodical Parallel Decoding, which leverage historical tokens to improve forecasting. Based on the two techniques above which fully leverage the inductive bias of periods inherent in time series, LightGTS uses a lightweight model to achieve outstanding performance on general time series forecasting. It achieves state-of-the-art forecasting performance on 9 real-world benchmarks in both zero-shot and full-shot setting with much better efficiency compared with existing time series foundation models

LightGTS: A Lightweight General Time Series Forecasting Model
Yihang Wang" *1
Yuying Qiu
Peng Chen
Yang Shu Chenjuan Guo
Zhongwen Rao Lujia Pan
Bin Yang'
Abstract
0.52
Timer NSE 0.4%6
Existing works on general time series forecasting build foundation models with heavy model param- eters through large-scale multi-souree pre-training. These models achieve superior generalization abil- ity across various datasets at the cost of signif- icant computational burdens and limitations in resource-constraing scenarios. This paper intro- duces LightGTS, a lightweight general time series forecasting model designed from the perspective of consistent periodical modeling. To handle di- verse scales and intrinsic periods in multi-source pre-training, we introduce Periodical Tokenization, which extracts consistent periodic patterns across different datasets with varying scales. To better utilize the periodicity in the decoding process, we further introduce Periodical Parallel Decoding, which leverages historical tokens to improve fore- casting, Based on the two techniques above which fully leverage the inductive bias of periods inherent in time series, LightGTS uses a lightweight model to achieve outstanding performance on general time series forecasting. It achieves state-of-the-arr forecasting performance on 9 real-worid bench- marks in both zero-shot and full-shot settings with much better efficiency compared with existing time series foundation models.
0.47
0.403 Paramatenn 700M
Average MSE
MORBA
MS2:
0.37
Ugmi0
NS2.0.371 Paranasnen 45GM
0.32
Ravametera 1:3M
Lighttt--rr1 Paramatinc 4M
0.27
10 Number of parameters (millions)
100
1000
Figure 1. Comparison of model sizes and average zero-shot perfor- mance across seven benchmark datasets between LightGTS and the state-of of-the-art TSFMs.
datasets, several Time Series Foundation Models (TSFM) have emerged (Liu et al., 2024; Woo et al., 2024a; Shi et al., 2024), demonstrating promising potential. However, the generalization capability of existing TSFMs largely depends on massive pre-traine pre-training data and large model parameters as shown in Figure 1, resulting in high computational costs and low efficiency.
Although both language and time series sequential data, unlike language which uses word tokens as basic elements, time series elements can vary substantially and exhibit distinctive characteristies. Specifically, scale refers to the sampling rate of time series, e.g., sampling every 15 mins or every hour, and intrinsic period reflects the time interval, e.g. daily, that pattern repetitively appears in the real-world. Meanwhile, different scales affect the number of data points that appear in an intrinsic period, referred to cycle length, as shown in Figure 2(a). In multi-source time series pre- training, this scale-dependent variation necessitates models to learn consistent representations of real-world periodic patterns across different cycle lengths, a core demand for reliable forecasting as evidenced by the critical role of periodic modeling (Lin et al., 2024b;a).
1. Introduction
Time series forecasting is widely applied across various domains, including energy, meteorology, education, finance, and transportation (Wu et al., 2021; 2023; 2024; 2025c). Traditional time series forecasting approaches typically use task-specific statistical or deep learning models in an end-to- end manner (Wu et al., 2025a; Qiu et al., 2025b; Wu et al., 2025b). Recently, with collection large-scale time series
"qqual contribution East China Normal University, Shanghai, China Huawei Noah's Ark Lab, Shenzhen, China. Correspon- dence to: Chenjuan Guo <cjguo@ wcn..ed..c..
However, the existing TSFMs adopt fixed tokenization, where each token contains fixed number of data points, making it struggle to handle diverse scales and intrinsic periods in multi-source pre-training. Specifically, fixed to- kenization leads to varying information density of tokens
Proceedings of the 42nd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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LightGTS: A Lightweight General Time Series Forecasting Model
Point Embedding
Fixed Patch Embedding
Periodical Patch Embedding (ours)
Point Embedding
Fixed Patch Embedding
Periodical Patch Embedding
ETTh2 Scale Hourly Cyclo langth
Intrinsic period [ 24 Haurs)
ETTm2 Scale = 15 min Cycle length 96
Solar Scale 10 min
Cycle length 144
(a) The illustration of three tokenization methods
(b) The case study of training on ETThi (Hourly, Cyele length= 24) and testing on datasets with different scales and cyele lengths
Figure 2. (a) The illustration of three tokenization methods (Point embedding. Fixed patch embedding, Periodical patch embedding). For example, ETTh2 and ETTm2 share the same daily intrinsic period, but their cycle lengths differ due to differences in scale. (b) The case study of training on ETThl and testing on datasets with different scales and cycle lengths, all three tokenization methods recognized the intrinsic period on the same-scale datascts. However, only periodical tokenization successfully transferred to datasets with different scales,
across different scales, resulting in inconsistent feature rep- resentations. Additionally, it also disrupts the continuity and structural integrity of periodic patterns. To illustrate this point intuitively, we conducted case study shown in single-scale dataset,
To better leverage the periodic patterns in the decoding process, we introduce a non- con-autoregressive decoding method, called periodical parallel decoding. Specifically, we initialize the decoder input with the last token generated by the encoder, consolidating all historical information. The key insight behind this design is that the last token not only maintains temporal continuity with future predictions but also leverages the structural consistency between historical and forecast horizons, enabling the effective extrapolation of periodic patterns and generating accurate predictions. In addition, the decoder outputs the predictions in parallel, which avoids cumulative errors and reduces computational cost.
Figure 2(b). After pre-training the model using the fixed tokenization recognizes the intrin- sic period within the same scale, but significantly performs worse when transferred to datasets with different scales. This highlights how the fixed tokenization limits the model's abil- ity to leverage time series inductive biases related to scale and intrinsic period, hindering the generalization ability and necessitating more parameters, which in turn increases computational costs and reduces efficiency.
The two techniques above enable the model to fully leverage the inductive bias inherent in time series data, significantly reducing the model's parameter size and lowering the com- putational resource requirements. As shown in Figure 1, LightGTS achieves state-of-ther -ott-e--rtttttttt- prediction performance with fewer than 5 million trainable parameters, making 10 to 100 times smaller than its counterparts.
In this paper, we aim to leverage the inherent inductive biases of scale-invariant intrinsic periods in time series data to design an efficient TSFM architecture. To achieve this, we propose LightGTS, which effectively utilizes such an inductive bias through adaptive periodical tokenization and periodical parallel decoding, compressing the model's parameter size while ensuring high performance.
In summary, our contributions in this paper are as follows:
To model intrinsic period consistently across different scales, we propose periodical tokenization, where the time series is adaptively divided into patches based on the cycle length, ensuring that each token captures a complete intrinsic period. Since the intrinsic period remains constant regardless of the scale, this approach ensures that the periodic patterns are consistently captured, and more importantly, the semantic information within each token remains aligned across differ- ent scales and cycle lengths. Furthermore, an embedding module with fixed projection cannot handle varying cycle lengths in multi-source time series pre-training, so we intro- duce a flex projection layer to address this issue. As shown in Figure 2(b), the periodical tokenization allows LightGTS to effectively generalize to datasets with varying scales and cycle lengths, improving the flexibility and adaptability of the model.
We propose novel periodical tokenization that adap- tively splits patches based on the intrinsic period of the dataset, naturally extracting consistent periodic patterns across different scales.
We further propose a simple and effective periodical parallel decoding which not only better leverages the pe- riodicity of time series data but also avoids cumulative errors and reduces the computational cost.
Based on the techniques above, we present Light- GTS, which fully leverages the inductive bias of time series data, making it achieve state-of-the-art predictive accuracy with less trainable parameters. Moreover, our code and pre-trained model check- points are available at https: / / wwg.gttt.bh... com/ decisi wtw.iiiinnneeeenneeeeeemmmm witggennn//igghTS..... GTS
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LightGTS: A Lightweight General Time Series Forecasting Model
2. Related Work
3. Methodology
2.1. Time Series Forecasting
Problem Formulation Given a multivariate time series 1 where each x²_ E R is sequence of observations. L denotes the look-back window and C denotes the number of channels. The forecasting task is to predict the future values Y, = ( IC where F denotes (11++))
Early time series forecasting (TSF) methods relied on sta- tistical techniques like ARIMA (Box & Pierce, 1970) and VAR (Godahewa et al., 2021a). With machine learning advancements, methods such as GBoost (Chen & Guestrin, 2016) and LightGBM (Ke et al., 2017) emerged but re- quired manual feature engineering. Leveraging the rep- resentation learning capabilittes of deep neural networks (DNNs), models like Pathformer (Chen et al., 2024), and PSt (Nie et al., 2023) have surpassed traditional meth- ods in forecasting accuracy. Recently, LLM-based methods like Time-LLM (Jin et al., 2023) and GPT4TS (Zhou et al., 2023) promise by leveraging L.LMs' capabilities to capture complex time series patterns. Additionally, pre-training on multi-domain time series data has gained significant attention, with notable approaches such as MOIRAI (Woo et al., 2024b) and UnITS (Gao et al., 2024), demonstrating promising results.
X, 1
the forecast horizon. Y, = {x (2++ ) is the ground truth. The general time series forecasting model is pre-trained with multi-source datasets D Prre-train = (X² Y f=l" where N is the number of datasets. For the downstream task, the model is fine-tuned with a training dataset Duain = { (Xtrain, y)min),, and is tested with Dust = {( y)= to predict Ylea where Dpre-trinn Dirain and Dies are pairwise disjoint. Alternatively. the model could be directly tested using Deest without fine-tuning with Drain to predict Prest
3.1. Architecture
As shown in Figure 3, LightGTS enhances time series mod- eling through periodical tokenization, which comprises two coordinated components: (1) adaptive Periodical Patching to segment sequences with different scales into period patches, and (2) the Flex Projection Layer to embed period patches with various lengths into shared semantic space. Integrated with the Transformer Encoder- Decoder, this approach first identifies intrinsic periodicities to generate period patches. The Flex Projection Layer then dynamically adjusts patch em- bedding weights, transforming diverse-length patches into dimensionally consistent tokens while retaining periodic semantics.
2.2. Tokenization in Time Series Foundation Models
Tokenization strategies are essential for TSFMs to transform raw data into structured input. The two primary methods, Point Embedding and Fixed Patch Embedding, offer distinct advantages. Point Embedding based models (Ansari et al., 2024) encodes individual time steps as distinct token, preserving fine-grained details for short-term dependencies but struggling with long-term patterns and noise. Fixed Patch Embedding segments the time series into fixed-length patches and embeds each patch single token. This tokenization technique improves computational efficiency, and captures aggregated patterns, making it well-suited for models such as Timer (Liu et al., 2024) and TimesFM (Das et al., 2023). However, neither the fixed tokenization above can deal with the varying scales and intrinsic periods in multi-source time series pre-training, limiting the generalization of the TSFMs.
Once the patches are embedded into tokens, the tokens are then passed into the Transformer encoder to model the periodical patterns within the input time series. Notably, instead of relying on autoregressive methods, we employ a periodical paraliel decoding approach(PPD) to construct the input for the Transformer decoder. This not only allows for more efficient and parallelizable processing of the se- quence, but also better accommodates periodic modeling by automatically aligning periodic features between input and output sequences. Finally, the tokens generated by the Transformer decoder are transformed into prediction results.
long-term dependencies and Transformer-bast
2.3. Decoding in Time Series Foundation Models
Decoding strategies influence how TSFMs generate future values. Key approaches include: i) Autoregressive decod- ing (Shi et al., 2024; Ansari et al., 2024). where models predict sequentially, but suffer from slow inference and error accumulation. ii) MLP decoding, which predicts all future values simultaneously using flatten head, allowing parallel computation, but lacking flexibility for arbitrary forecasting horizons. iii) Masked autoencoders (Goswami et al., 2024; Gao et al., 2024), which train models to reconstruct missing values, improving temporal representation but relying on reconstruction loss and requiring large-scale data. Unlike these, our periodical parallel decoding combines flexibility and efficiency, while also making better use of the periodicity in time series data.
1.1.1. PERIODICAL TOKENIZATION
Periodical Patching: For the simplicity of notations, we use a univariate time series for description, and the method can be easily extended to multivariate cases by considering each variable independently. Given a collection of time series from multi-source datasets where each x R. exhibits its own intrinsic period during pre-training, first identify the cycle length P (data points per intrinsic period) for each x via periods- finding.
P = PeriiosFFindingx
(I)
3

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LightGTS: A Lightweight General Time Series Forecasting Model
Periodical Tokenization
Flex Projection Output Layer
Periodical Parallel Decoding
|0000
1000000
Transformer Encoder (No masking)
I.
Tokesa
Flet Resize
Flox Rested
Tokero
Patch Embbeding Weights
Transformer
Decoder Add&NNrm
e (T)
Feed-Forward
Reweighting
Add&Norm
Flex Projection Input Layer
Paiching
Pl
Porieds Finding
Patching
Cross Attention
L
Periodical Patching
Causal Attention
K = F/P
Replicate K times
m
mmw
Figure 3. LightGTS architecture.
It is worth noting when prior knowledge of the input series is available, the cycle length can be inferred using information such as the sampling rate. In the absence of prior knowledge, the cycle length can also be deduced using methods such as Fast Fourier transform (FFT) (Wu et al., 2022).
handle the input x' with a different patch size P'. However, this simple linear interpolation in embedding projection introduces substantial distortions in token representations and causes x # x' 0'. Such changes hinder the ability to adapt a pre-trained backbone, designed for fixed patch size, to process inputs with varying patch sizes effectively.
After obtaining the cycle length P. the input series is seg- mented into non-overlapping period patches X, E R PxN where N is the number of the patches, N = LL.PJ. Each patch aligns precisely with the data's intrinsic periodic in- terval, ensuring that one patch encapsulates a full cycle. By doing so, time series of varying scales are interpreted within unified period-aligned semantic space, eliminating inter- ference from varying sampling rates and enabling coherent cross-source pattern learning during pre-training.
We then discuss the proposed Flex Projection to address such inconsistency of token representations across different scales. Note that the linear interpolation can be formalized as a linear transformation:
Interp(x) = A
(2)
where A E R PxP" represents the linear transformation matrix that resizes a vector x with length P to length P' by linear interpolation. The ideal objective of Flex Projection is to preserve token consistency across scales by deriving adjusted embedding weights 0' that satisfy when processing inputs varying scales. Thus, hope to find new set 0' under the following optimization objective:
Flex Projection Layer: Each period patch preserves local periodic semantic information after segmenting the time series using the Period Patching mechanism. Then, the patch embedding projection transforms the period patches into tokens. However, time series from multi-source datasets exhibit diverse intrinsic periods and scales, leading sig- nificant variation in patch sizes. Therefore, the fixed patch embedding projection struggles to process varying patch sizes. A straightforward approach is to resize the weights of patch embedding projection directly using methods like linear interpolation to accommodate different patch sizes. However, the simple linear interpolation may introduce bi- ases into the resulting tokens, which may degrade model performance, as discussed below.
x' 0
0' = arg BargminB,xxlll 0 xA 0'1121.
(3)
where X is some distribution over the input patches, -IF is the Frobenius norm of vector. In Section 3.2, we ex- tend our analysis to account for shifts in patch distributions and theoretically demonstrate that the adjusted embedding weights must satisfy 0' = 5- (A)) to preserve token consis-
tency. The term ō = V pr is the upper bound of the variation in the variances between x and A, where ()* denotes the Moore-Penross pseudoinverse of the matrix. Thus, we define flex-resize as:
Consider processing the same dataset with two different scales, periodical patching on the dataset yields patches of two different sizes: x R and x' R..". Based on the scale difference, we assume a linear interpolation relationship between these patches and have x' Interpp" (x). Suppose we already have the original patch embedding weights 0 e R PxD tailored for projecting x. Then we want to get the embedding projection weights 6' forx' that satisfies 6 = x'. 0'. In a straightforward way, the original & should he resized through interpolation to obtain = Interp (0) E R'''D to
Flex-resize(0)f- = o
(4)
The flex-resize ensures the equivalence of patch embeddings across different patch sizes while preserving the stability of statistical characteristics. Leveraging the flex-resize, we propose the Flex Projection Layer which adapts to vary- ing cycle lengths without compromising the performance.

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LightGTS: A Lightweight General Time Series Forecasting Model
Specifically, we define two underlying parameter matri- ces for the input layer and output layer: de PRD and Oa "D'" where P represents predefined reference patch size, and D is the latent dimension. These learnable parameters are dynamically resized with the resize transfor- mation 6- (A)* E P during the forward pass to match the required patch size for each time series. Using the re- sized patch embedding, we then map the patches Xp into the Transformer latent space to obtain the tokens X, DDXN
R Dx1 resulting in H (hy) e RD I..... K, where K [F/P] is the number of tokens corresponding the prediction length. Additionally, the influence of the last token on the predicted sequence decreases as the prediction length grows. To account for this, we apply a reweighting function w(T) to the tokens in H, where T denotes the position index of each token. Thus, the set of tokens H weighted as w(j) hy. Ultimately, all tokens are simultancously input into the Decoder:
X Xp (f
(5)
Z = Decoder ({w(i) (()()))),EE) w(T) = ex
(8)
3.1.2. ENCODING AND DECODING
Y = Flax Z.
Similarly to the original Transformer, our encoder and decoder modules are composed of FerwaForward Networks and Multi-Head Attention modules. Notably, we leverage Rotary Positional Encoding (RoPE) (Su et al., 2021) in the attention modules to enhance the modeling of relative positional information between tokens.
where Z E R is the output of the Decoder. Finally, predictions are obtained through the Flex Projection Layer.
3.1.3. Loss FUNCTIONS
In alignment with current mainstream practices in the field, we adopt the classic Mean Squared Error (MSE) as the loss function for LightGTS. This function measures the discrepancy between the predicted values Y and the actual ground truth Y. It is formulated as:
Encoding: After obtaining the projected tokens X, (x!.xX....xx .... E RDDN, where the superscript/ in x de- notes the i-th token, we incorporate RoPE into the attention mechanism to represent the relative positional information across different tokens. For brevity, we leave layers, atten- tion head indices, and the scaling factor. Let x and x be the query and key vectors at positions and j. respec- tively. The transformed query and key vectors are Wox! and Wxx!, where Wo E DxD and Wx E RR are learn- able projections for queries and keys. The rotation matrix R E NNN is then applied to adjust their relationship, and the similarity score computed as:
LMSE = 1|Y &
(10)
3.2. Theoretical Analysis
In Section 1, we have described that linear interpolation may change the effectiveness of patching embedding:
Interp(x)) A,
(11)
S.j = (Wox.) (Wkx))...
(6)
where A RPP represents the linear mapping matrix. This operation resizes vector with length P to length P' by linear interpolation. To pursue the equivalence of patching embedding, we hope to find a new set of O' under the optimization problem defined by Theorem 3.1.
The similarity scores Sij E R are then normalized using the Softmax function and combined with the value vectors Wyx' to compute the attention output, where Wv E D
exp(S,)
Attn; = Σ E. ) (Wvx)).
(7)
Theorem 3.1. Patching embedding can be treated as linear projection on patch with parameters 0. To preserve token consistency across seales, 0' is solved for keeping the minimum Euclidean distance between projected vectors:
Finally, each token is processed through Ford-Forward Network (FFN) to extract features, resulting in the latent representation E = {ej} E ERDNN.
6' arg minE [l[x xA xA-1
(12)
Periodical Parallel Decoding: Periodical tokenization ef- fectively extracts periodical information. To further leverage the periodical information in the decoding process, we pro- pose periodical parallel decoding. novel auteeervreeesssvvve decoding method. Given that the last token generated by the encoder not only retains the relevant intrinsic periodic characteristics but also consolidates historical information, we use it as the decoder's 's input to guide prediction process.
where X is some distribution over the patches, || |IF is the Frobenius norm of a vector. Furthermore, to keep the distributional consistency, we refine the optimization problem as Proposition 3.2.
Proposition 3.2. Time series pre-trained models utilize normalization during pretraining. thus they learn fixed distribution over patches which is susceptible to slight effects from interpolation. Therefore, additional normalization
In contrast to autoregressive decoding, we replicate the last token of the latent representation, denoted as eN E
5

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LightGTS; A Lightweight General Time Series Forecasting Model
needed to align the distributions of projected patches with the pre-trained backbones:
nine widely recognized forecasting benchmarks as target datasets, all strictly exclusive from the pre-training datasets. These benchmarks include Weather, Traffic, Electricity, So- lar, Exchange, and the four subsets of ETT, spanning multiple domains to validate model generalizability.
0' arg min 0 no)m(xA) -0'11))
(13)
Since Revin normalization (X- (O) I) and linear interpo- lation does not change the mean values, the norm operation can be further expressed as maltiplying by constant ô to eliminate the variation in variances:
Baselines. We select five foundation models for compari- son in zero-shot setting, including Timer (Liu et al., 2024), MOIRAI (Woo et al., 2024b), Chronos (Ansari et al., 2024), TimesFM (Das et al., 2023). Time-MoE (Goswami et al., 2024). We also select state-of-the-ar deep time series mod- els as baselines in full-shot setting, including PDF (Dai et al., 2024), iTransformer (Liu et al., 2023), Pathformer (Chen et al., 2024), FITS (Xu et al., 2023). TimeMixer (Wang et al., 2024a), and PatchTST (Nie et al., 2022).
0' = arg minna..-....... x
<|| |l|x 0 oxA- 011
(14)
= arg minBx-XX x [l|x (0- - 5A0) 11221
(15)
arg minEx-x 6A XJ - 6A0')]
(16)
= arg min (0 - 6'6'' " (xx" [ (60 5A0')
(17) Setup. Following prior studies, we use Mean Squared Error (MSE) and Mean Absolute Error (MAE) evaluation metrics. All methods predict future values for lengths F = (96, 192, 336. 7203. We have pre-trained two variants of LightGTS: LightGTSS-iny with 1 million parameters and LightGTS-min with 4 million parameters. Additional implementation details are provided in Appendix A.
6'
arg minl16 6/
(18)
In Proposition 3.2, Ex-x(xxX] denotes the uncentered co- variance matrix, ||r11 = ''EV is the quadric form of v. Since we only consider the case X = N(O, I). Ex-x [xx"] ] is also the covariance matrix. And the optimization objective can be formulated as a least squares solution to a linear system of equations:
4.2. Zero-shot Forecasting
To ensure a fair comparison, we conduct zero-shot predic- tions for each foundational model on downstream datasets not included in their pre-training data. As shown in Table 1, LightGTS-min -ini consistently achieves the statc-of-the-at per- formance, delivering an average MSE reduction of over 30% compared to the most competitive baselines. Remarkably, even with fewer parameters, LightGTTS-tiny still outperforms across the majority of datasets, achieving an average MSE reduction of 27%. Furthermore, LightGTS demonstrates superior performance compared to baselines with hundreds of millions of parameters. Specifically, it achieves average MSE reductions of 27% and 28% compared to Chronos and MOIRAL, respectively, and relative improvement of 17% over Time-MoE. This highlights LightGTS's ability to effectively exploit the inherent inductive biases of time series data, enabling exceptional performance even with significantly fewer parameters.
0' arg minl 11
(19)
Singular value decomposition (SVD) technique is widely applied to obtain approximate or exact solutions to the aforementioned optimization problem, with the general solution being related to the Moore-Penrose pseudoinverse:
0' = = (A)*0.
(20)
where the 5 = V pr is the upper bound of the variation in the variances between and x A.
In summary, the process can be treated as conducting resize transformation 8 (A)+ on the weights e of projection layers.
It works in a no-learning way by solving the optimization problem above, which saves computational overhead.
4.3. Full-shot Forecasting
4. Experiments
As shown in Table 2, we present the results of the LightGTS in full-shot and zero-shot settings, and compare with other baselines in full-shot setting. Key observations are sum- marized as follows. First, as general forecasting model, LightGTS achieves superior performance compared to the six state-of-the the baselines with full-data training, achiev- ing an average MSE reduction of 7%. Second, we observe that LightGTS in zero-shot setting significantly outperforms the baselines in full-shot setting across five datasets. This observation validates the strong transferability of LightGTS pre-trained on large multi- source data.
4.1. Experimental Setup
Pre-training datasets. To pre-train a general time series forecasting model effectively, we collect substantial number of publicly available datasets spanning diverse domains, including energy, nature, health, transportation, web, and economics. Detailed information about these datasets is provided in Appendix A.I.
Evaluation datasets. ensure comprehensive and fair com- parisons across different models, we conduct experiments
6

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LightGTS: A Lightweight General Time Series Forecasting Model
Table Full results of zero-shoo shot forecasting experiments. The average results all predicted lengths are listed here. Lower MSE or MAE values indicate better predictions, A dash ('-) denotes datasets included in the model's pretraining and therefore excluded from testing. Red: the best, Blue: the 2nd best.
Models
LightGTS-tiny
LightGTS-min
Timer (2024)
MOIRAI (2024)
Chronos (2024)
TimesFM (2024)
Time-Moli (2025)
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
ETTml
0.345
0.378
0.327
0.37
0.768
0.568
0.39
0.389
0.551
0.453
0.435
0.418
0.376
0.406
ETTm2
0.249
0.318
0.247
0.316
0,315
0.356
0.276
0.32
0.293
0.331
0.347
0.36
0,315
0.365
ET
0.401
0.424
0.388
0.419
0.562
0.483
0.51
0.469
0.533
0.452
0.479
0.442
0.394
0.420
ETTh2
0.362
0.397
0.348
0.395
0.370
0.400
0.354
0.377
0.392
0.397
0.400
0.403
0.403
0.415
Truffic
0.610
0.399
0.561
0
0.613
0.407
0.615
0.421
Weather
0.219
11.26h
0.208
0.256
0,299
0.313
0.275
0.288
0.309
0.270
0.300
Exchange
0.345
0.395
0.347
0.396
0.392
0.425
0.385
0.417
0.370
0.412
0.390
0.417
0.432
0,454
Solar
0.219
0.305
0.191
0.271
0.771
0.604
0.714
0.704
0.393
0.319
0.500
0.397
0,411
0.428
Electricity
0.233
0.319
0.213
0.308
0.297
0.375
0.188
0.273
Table 2. The results of LightGTS-mini in zero-shot and full-shot sctting and other baselines in full-shot setting. The average results of all predicted lengths are listed here. Lower MSE or MAE values indicate better predictions. Red: the best, Blue: the 2nd best.
LightGiS mini
LightGTSS mini
PDF
iTrnnformer
Pathformer (2024)
FITS
TimeMXier (2024)
PatchTST (2023)
Models
(zero-shot)
(full-shot)
(2024)
(2024)
(2024)
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSB
MAE
MSE
MAE
ETTml
0.327
0.370
0.321
0.361
0.342
0.376
0.347
0.378
0.357
0.375
0.357
0.377
0.356
0.380
0.349
0.381
ETTm2
0.247
0.316
0.239
0.303
0.250
0.313
0.258
0.318
0.253
0.309
0.254
0.313
0.257
0.318
0.256
0.314
ETTh1
0.388
0.419
0
0.413
0.407
0.426
0.440
0.445
0.417
0.426
0.408
0.427
0.427
0.441
0.419
0.436
ETTh2
0.348
0.395
0.335
0.377
0.347
0.391
0.359
0.396
0.360
0.395
0.335
0.386
0.347
0.394
0.351
0.395
Traffic
0.561
0,381
0.393
0.259
0.395
0,270
0.397
0
0.416
0,264
0.429
0,302
0.410
0.279
0.397
0.275
Weather
0.208
0.256
0.207
0.244
0.227
0,263
0.232
0.270
0.225
0.258
0.244
0.281
0.225
0.263
0.224
0.261
Exchange
0.347
0.396
0.322
0.383
0.350
0.397
0.321
0.384
0.384
0.414
0.349
0.396
0.385
0.418
0.322
0.385
Solar
0.191
0.271
0.179
0.220
0.200
0.263
0.202
0.260
0.204
0.228
0.232
0.268
0.203
0.261
0.200
0.284
Electricity
0.213
0.308
0.156
0.248
0.160
0.253
0.163
0.258
0.168
0.261
0.169
0.265
0.185
0.284
0.171
0.270
4.4. Efficiency Advantages of LightGTS
4.5. Ablation Studies
In addition to its excellent prediction performance, another notable advantage of LightGTS is its lightweight nature. Pre- viously, Figure visualized the parameter-performance com- parison of LightGTS with other TSFMs. Table 3 presents a more comprehensive efficiency comparison between Light- GTS and other TSFMs in terms of both static and runtime metrics. It is evident that LightGTS significantly outper- forms other models in terms of static metrics such as the number of parameters and Multiply-Accumulate Operations (MACs), being over ten times smaller than the next best model. This characteristic allows LightGTS to be deployed on devices with limited computational resources. Further- more, in terms of runtime metrics such as Max Memory and Inference Time, LightGTS significantly outperforms other TSFMs, rivaling existing small models (i.c., PatchTST).
Effectiveness of Periodical Tokenization To validate the effectiveness of periodical tokenization, we conducted exper- iments comparing fixed patching and periodical patching on models with different decoding methods. The results, shown in Table 4, demonstrate that periodical patching consistently outperforms fixed patching across all datasets. Furthermore. periodical patching provides significant improvements re- gardless of the decoding method used, highlighting its strong generalization capability.
Table 4. Ablations on key components of LightGTS in zero-shot setting, including periodical tokenization, and periodical parallel decoding. The average results of all predicted lengths are listed.
Dataset
ETT-sg
Weather
Flletriity
Traffic
Decoding
Patching
MSE
MAE
MSE
MAE
MSB
MAE
MSE
MAE
AR
Fixed
0.442
0.430
0.265
0.293
0.231
0.326
0.630
0.411
Periodical
0.341
0.381
0.226
0.270
0.229
0.634
0.410
Table Static and runtime performance metrics of LightGTS and other baselines on the ETTml dataset, evaluated with forecast horizon of 720 and batch size of 1.
MAE
Pixed
0.537
01489
0.339
0.349
0.372
0.428
0.803
0.534
MAE
Periodical
0.388
0.477
0.260
0.301
0,322
0.392
0.746
0.484
Fixed
0.427
0.262
0.288
0.226
0.621
0.403
PPD
Periodical
0.328
0L375
0.208
0.256
0.213
0.308
0.561
0.381
Models
Parameters
MACs
Max Mcm.(MB)
Inference Time (5)
Time MolE
453 M
G
14131
TimesPM
200 M
6
1395
0.16
Effectiveness of Periodical Parallel Decoding To further validate the effectiveness of our periodical parallel decoding (PPD) method, we conducted an ablation study by replac- ing it with mainstream autoregressive (AR) decoding and
Chronos
700 M
92327.9G
10269
34.33
MOIRAI
300 M
97.36
2009
0.1
Timer
67.4 M
52.6
1435
0.08
PatchTST
6.3M
225 M
672
0.01
LighGTS
4M
213 M
713
0.01
7

---

LightGTS: A Lightweight General Time Series Forecasting Model
masked autoencoder (MAE) decoding. The results, shown in Table 4, indicate that PPD consistently outperforms both AR and MAE decoding under both fixed patching and peri- odical patching strategies. Among the three methods, MAE achieved the poorest performance, likely due to a task gap between its upstream reconstruction objective and the down- stream prediction task. Furthermore, we observed that PPD only slightly outperforms AR when using fixed patching, primarily because PPD avoids the accumulation of errors in long-step predictions. However, with periodical patch- ing, the performance gain of PPD) over AR becomes more pronounced, as PPD better exploits the inherent periodicity.
the same datasets (ETT) and ETT2) with different sampling granularities while predicting the same time horizon (96 hours) in zero-shot setting. As shown in Figure 4, the re- sults show that Timer and Time-MoB exhibit significant performance variation when faced with different sampling granularities, whereas LightGTS maintains stable perfor- mance. This further supports the idea that existing time series foundation models are unable to handle the variations in scale within time series datasets. In contrast, Light- GTS, by understanding the time series from its intrinsic period, remains unaffected by changes in dataset scale, thus maintaining stable performance across different sampling granularities.
4.6. Model Analasis
Impact of the Reference Patch Size
ETT2
ETTI
0.99
0.50
LightGTG introduces a hyperparameter P* in the flex projec- tion layer, namely the predefined reference patch size before resizing. To evaluate its impact on the performance of Light- GTS, we conducted an ablation study using four different reference patch sizes. The experimental results presented in Table 5 demonstrate consistently stable performance across all evaluated patch sizes, indicating that the model exhibits strong insensitivity the selection of p", Therefore, we the default value to 48 in all experiments empirically.
0.37
MSE
MSE
0.79
0.15
0.28
0.53
0.223
0.55
Sampling Granularity
Sampling Grunularity
LightGTS
Time--Mo
Timer
Figure 4. Comparisons of robustness across different sampling granularities between LightGTS, Timer, and Time-MoB in the zero-shot setting.
Table MSE results of LightGTS with varied hyperparameters of reference patch size p The average results of all predicted
lengths are listed here.
Models
ETT-avg
Weather
Electricity
Traffic
Matric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
Representation Learning of the Periodical Tokenization As shown in Figure 5, we compare token representation sim- ilarity between Timer (fixed patch size=96) and LightGTS solar with daily intrinsic period under varying sampling granularities. At 10-minute sampling (cycle length= 1 144), Timer's 's fixed patch fails to align with the full cycle, resulting in low inter-token similarity. Conversely, at 30-minute sam- pling (cycle length=48), patch size accidentally spans two full cycles, leading to high similarity. This inconsistency reveals the limitation of fixed tokenization in multi-scale temporal modeling. In contrast, LightGTS uses periodical tokenization, which produces the same number of tokens re- gardless of the sampling granularities, leading to consistent token representations across sampling granularities.
p' 24
0.335
0,380
0,213
0.262
0.217
0.312
0.563
0.384
p" = 48
0.328
0,375
0.208
0.256
0.213
0.308
0.561
0,381
p" = 96
0.331
0.375
0,210
0.256
0.217
0.307
0.566
0,388
0.334
0.377
0,212
0.258
0.212
0.304
0.566
0.385
Impact of the Replicated Token Choosing Since the initial- ization of the decoder input is crucial for non-autoregressive decoding (Gu et al., 2017), we select the last encoder to- ken as the input. To validate this choice, we experiment with replacing it using other tokens, such as the learnable embedding, the CLS token, and the mean of the encoder tokens. As shown in Table 6. the last encoder token yields the best performance, likely due to its better alignment with the periodicity and greater relevance to the prediction task.
Table 6. MSE results of I. LightTTS with different replicated tokens. The average results of all predicted lengths are listed here
110min
130min
110min
130min
Dotsset
ETT-ag
Weather
Flectricity
Traffic
Metric
MSE
MAB
MSE
MAE
MSE
MAB
MSE
MAE
LighiCTSS-leam
0.342
0.383
0.278
0325
0.231
0.326
0.627
0.410
LightGTS-els
0.343
0.385
0.341
0.371
0.234
0.634
LightGTS mean
0.404
0.133
0,328
0.350
0.273
0.361
0,703
0.464
(4) Timer (Fixed Tokenization)
(b) LightGTS (Periodeial Tokenization)
LighaGTSS-lstt
0.328
0.375
0.208
0.256
0.213
0.308
0.561
0.381
Figure 5. Similarity of token representation across various sam- pling granularities in Fixed (Timer) versus Periodical (LightGTS) Tokenization.
Robustness across Different Resolusions our experi- ments, we evaluated Timer, Time-MoF, and LightGTS on
8

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LightGTS: Lightweight General Time Series Forecasting Model
5. Discussion
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Impact Statement
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Acknowledgements
This work was partially supported by National Natural Sci- ence Foundation of China (62372179, 62406112). Chenjuan Guo is the corresponding author of the work.
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LightGTS: Lightweight General Time Series Forecasting Model
A. Implementation Details
A.1. Pre-training Datasets
We incorporate a diverse range of multi-source datasets for pre- pre-training, which include portions from the Monash (Godahewa al., 2021b), UEA (Bagnall al., 2018), and UCR (Dau al., 2019) time series datasets, as well additional classic datasets (Zhang al., 2017; Wang al., 2024b; Liu al., 2022; McCracken & Ng, 2016; Taieb al., 2012). The complete list of pre-training datasets is shown in Table 7. It's important note that there is no overlap between these pre-training datasets and the target datasets. Additionally, while the weather dataset in the pre-training set is univariate, the weather dataset in the target task is multivariate. The datasets used for pre-training are divided into six categories based on their domains: Energy, Nature, Health, Transport, and Web. The datasets exhibit a wide range of sampling frequencies, from millisecond intervals to monthly data, reflecting the complexity and variability of real-world applications. For all pre-training datasets, we split them into univariate sequences and train them in a channel-independent manner.
Table 7. List of pretraining datascts.
Domain
Dataset
# Frequency
Time Pionts
Source
Aus. Electricity Demand
Half Hourly
1155264
Monash (Godahewa al., 2021b)
Wind
Seconds
7397147
Monash (Godahewa et al., 2021b)
Energy
Wind Farms
Minutely
172178060
Monash (Godahewa ct al., 2021b)
Solar Power
4 Seconds
7397222
Monash (Godahewa al., 2021b)
London Smart Meters
Half Hourly
166527216
Monash (Godahewa al., 2021b)
Phoneme
2160640
UCR(Dau et al., 2019)
Figen WogenWorms
27947136
UEA (Bagnall al., 2018)
PRSA
Hourly
4628448
(Zhang et al., 2017)
Temperature Rain
Daily
23252200
Monash (Godahewa ct al., 202
9457664
UCR (Dau al., 2019)
Worms
0.033 Seconds
232200
UCR (Dau al., 2019)
Nature
Saugeen River Flow
Daily
23741
Monash (Godahewa et al., 2021b)
Sunspot
Daily
73924
Monash (Godahewa al., 2021b)
Weather
Daily
43032000
Monash (Godahewa al., 2021b)
KDD Cup 2018
Daily
2942364
Monash et al., 2021b)
US Births
Daily
7305
Monash (Godahewa al., 2021b)
MotorImagery
0.001 Seconds
72576000
UEA (Bagnall al., 2018)
SelfRegulationSCPI
0.004 Scconds
3015936
UEA (Bagnall et al., 2018)
ScIfRegulationSCP2
0.004 Scconds
3064320
UEA (Bagnall al., 2018)
AtrialFibrillation
0.008 Seconds
38400
UEA (Bagnall al., 2018)
Health
PigArtPressure
624000
UCR (Dau et al., 2019)
PIGCVP
624000
UCR (Dau al., 2019)
TDbrain
0.002 Seconds
79232703
(Wang el al., 2024b)
Pems03
5 Minute
9382464
(Liu et al., 2022)
Pems04
5 Minute
5216544
(Liu al., 2022)
Pems07
Minute
24921792
(Liu al., 2022)
Transport
Pems08
5 Minute
3035520
(Liu et al., 2022)
Pems-bay
5 Minute
16937700
(Liu al., 2022)
Pedestrian Counts
Hourly
3132346
Monash (Godahewa et al., 2021b)
Web
Web Traffic
Daily
164855589
Monash (Godahewa et al., 202
FRED_MD
Monthly
77896
(McCracken & Ng. 2016)
Economic
Bitcoin
Daily
75364
Monash (Godahewa et al., 202
NNS
Daily
87801
(Taieb al., 2012)
12

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LightGTS: A Lightweight General Time Series Forecasting Model
A.2. Evaluation Datasets
We use the following 9 multivariate time-series datasets for downstream forecasting task: ETT datasets' contain 7 variates collected from two different electric transformers from July 2016 to July 2018. It consists of four subsets, of which ETTh1/ETTh2 are recorded hourly and ETTm m/ are recorded every 15 minutes. Electricity? contains the electricity consumption of 321 customers from July 2016 to July 2019, recorded hourly. Solar? collects production from 137 PV plants in Alabama, recorded every 10 minutes. Traffic* contains road occupancy rates measured by 862 sensors on freeways in the San Francisco Bay Area from 2015 to 2016, recorded hourly. Weather' collects 21 meteorological indicators, such as temperature and barometric pressure, for Germany in 2020, recorded every 10 minutes. ExchangeRate collects the daily exchange rates of countries. We split each evaluation dataset into ciiin-valiattion--e sets and detailed statisties of evaluation datasets shown in Table 8.
Table 8, The statistics evaluation datasels.
Dataset
Domain
Frequency
Timestamps
Spllit
# Dims
Intrinsic Period
# Cycle Length
ETTh1
Energy
hour
14400
6:2:2
7
Daily
24
ETTh2
Energy
hour
14400
6:2:2
7
Daily
24
ETTml
Energy
15 mins
57600
6:2:2
7
Daily
96
ETTm2
Energy
15 mins
57600
6:2:2
7
Daily
96
Electricity
Energy
mins
26304
7:1:2
321
Daily & Weekly
24 & 168
Solar
Energy
mins
$2560
7:1:2
137
Daily
144
Traffic
Traffic
hour
17544
7:1-2
862
Daily & Weekly
24 & 168
Weather
Environment
mins
$2696
7:1:2
Daily
144
Exchange
Economic
1 day
7588
7:1:2
A.3. Baselines
We select five foundation models for comparison in zero-shot setting, including Timer (Liu et al., 2024), MOIRAI (Woo et al., 2024b), Chronos (Ansari et al., 2024), TimesFM (Das et al., 2023), and Time-MoE (Goswami et al., 2024). In addition, we select the state-of-the-art models of deep time series models as our baselines full-shot setting, including PDF, iTrrnsformer (Liu et al., 2023), Pathformer (Chen et al., 2024), FITS (Xu et al., 2023), TimeMixer (Wang et al., 2024a), and PatchTST (Nie al., 2022). The specific code base for these models is listed Table 9:
Table Code repositories for baselines.
Model Types
Models
Code Repositories
Timer
https//githu..com/hann arge- Time-Time-aee Series Model
MOIRAI
https://ithhbb com/redoules//mirrui
Foundation model
Chronos
http://gihub..o//aaaaaoe www//mazono http://aooonccicccccc/memmmm forecasting
TimesPM
http:://ithub. com/ wom.goolee-eeseaccttnneeee
Time-Mol:
hups://github.. com/ l'me Mol/Time-MMi Mol:
PDF
hups://ithhbb com/Hunnk0626/PDF
ilranstormer
htlps://ithhbb httpe//wwwooommmm/////tfttttotte
Pathformer
Small Model
FITS
TimeMixer
http://gaaab..oom//vvuu////nnnie
PatchTST
I hntpss//gittub..mm//huuubbe com//zhoulaaoyy/ETTaaatstt
2
3 http:://dllac..o///d/d/ www..aa/o/////a/////////////
#https:/pemss.do..ca 005....0110109999999999200
$ http::/wwwwwwwwj....eeeeee/e
6 http:://dd..cm..oo////////a///// 04/.00111144220998222200000
13

---

LightGTS: A Lightweight General Time Series Forecasting Model
A.4. Setting
Pre-trainning We implemented LightGTS using Py Torch (Paszke et al., 2019), and all experiments were conducted on an NVIDIA A8000 80GB GPU. The optimization was performed using the ADAM optimizer (Kingma & Ba, 2014) with an initial learning rate of 5 x 10-4. A learning rate decay strategy reduction during pre-training. During pre-training, we use N = 10 as the number of historical tokens, K = 4 as the number of prediction tokens, P = 48 as the reference patch size, and the batch size is set to 8192. Detailed configurations and parameter counts of the pre-trained models involved in this paper are provided in Table 10.
applied using the StepLR scheduler to facilitate gradual
Downstream Forecasting downstream forecasting, we configure the model to perform periodical patching based on the cycle length, tailored the characteristics of each dataset. The number of historical tokens is set to 10, and the model is tasked with making predictions for target lengths of 96, 192, 336, and 720, respectively.
The "Drop Last" issue is reported by several researchers (Qiu et al., 2024; 2025a; Li et al., 2025). That is, in some previous works evaluating the model on test set with drop-last-True setting may cause additional errors related to test batch size. In our experiment, to ensure fair comparison in the future, we set the drop last to False for all baselines to avoid this issue.
Table 10. Detailed model configurations LightGTS and corresponding parameter counts.
Models
Encuder Layers
Decoder Layers
Model Dim.
FFN Dim.
Parameters
LightGTS-tiny
256
512
1.3M
LightGTS mini
3
3
256
512
4M
B. More Results and Analysis
B.1. Analysis of the Periods Finding
In this experiment, we investigate the effect of periodical finding methods. When prior knowledge is available or when there is sufficient data, we can treat the cycle length as known information. However, when prior knowledge is unavailable or data insufficient, we can use the Fast Fourier Transform (FFT) to determine the cycle length based on the input sequence. As shown in Figure 6, the key observations are follows:
When the data exhibits strong periodicity (e.g., Solar, Electricity, Traffic), the cycle length extracted by FFT aligns well with the actual period, ensuring stable model performance.
When the periodicity of the data is not pronounced (e.g., ETT, Weather), the cycle length extracted by FFT may not align with the intrinsic period, which can hinder model performance. However, LightGTS-FFT still outperforms the SOTA baselines.
When the data exhibits little to no periodicity (e.g., Exchange), intrinsic period modeling is not crucial for the model's s understanding of the time series. Therefore, regardless of the Periods Finding method used, its impact model performance is minimal.
Elactricity (F,
Traffic (F, 0.92)
ET
Weather
-0,67)
1.51
0210
MSS.
E211
0/11
Figure 6. Comparisons of the model performance between different Periodical Finding methods in zero-shot setting. The SOTA baselines refer to the hest-performing baseline results for each dataset. Fs means the seasonality strength for each dataset.
14

---

LightGTS: A Lightweight General Time Series Forecasting Model
B.2. Generality of the Periodical Tokenization
Periodical tokenization can serve plug-in, adapting TSFMs that use patching methods (such as Timer) without the need for retraining. We applied periodical tokenization to Timer and tested its predictive performance in the zero-shot setting with different resizing methods, including the lincar-resize and area-resize. The results, shown in Table 4, reveal that incorporating periodical tokenization significantly enhances performance across all resizing methods. Moreover, the flex-resize achieved a 19.23% improvement, outperforning the other two resizing methods by significant margin.
Table 11. Ablation MSE results of the Flex-resize. All results are collected with periodical patching. The "Boost" indicates the percentage of performance improvement after incorporating the different resize techniques.
Dataset
Weather
Solar
Horizon
96
192
336
720
96
192
336
720
Timer
0.190
0.261
0.332
0.385
0.591
0.689
0.831
0.972
Linear-resize
0.187
0.247
0,305
0.368
0.459
0,504
0.580
0.783
Boost
1.79%
5.22%
8.13%
4.36%
22.33%
26.89%
30.24%
19.42%
Arca-resize
0.186
0.246
0.304
0.367
0,461
0,506
0,581
0.782
Boost 2.23%
5.65%
8.41%
4.62%
21.93%
26.62%
30.08%
19.57%
Flex-resizee
0.178
0.238
0.297
0.357
0.425
0.488
0.558
0,671
Boost
6.24%
8.81%
10.54%
7.27%
28.05%
29.17%
32.85%
30.93%
C. Full Experimental Results
C.1. Zero-shot Forecasting
We provide all the results of the zero forecasting Table 12. As shown Table 10, we include nine representative real-world datasets, demonstrating that LighIGTS achieves state-of-the-art forecasting performance.
C.2. Full-shot Forecasting
Table 13 provides the comprehensive results in-distribution forecasting, showcasing the performance of LightGTS-ming in both zero-shot and full-shot settings, as well as other baselines in the full-shot setting. Notably, LightGTS demonstrates superior performance over all baselines in the full-shot setting. Moreover, in the zero-shot setting, LightGTS achieves competitive results, rivaling the full-shot performance of other baseline models.
C.3. Ablation Study
Table 14 presents the detailed results of the ablation studies for LightGTS in the zero-shot setting, including periodical tokenization and periodical parallel decoding.
15

---

LightGTS: A Lightweight General Time Series Forecasting Model
Table 12. Full results of zero-shot forecasting experiments. Lower MSE MAE values indicate better predictions. A dash (+') denotes datasets included in the model's pretraining and therefore excluded from testing. Red: the best, Blue: the 2nd best.
Models
LighiGTS-tiny
LighiGTS-mini
Timer
MOIRAI
Chronos
TimesFM
Time-MoE
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSB
MAE
0.307
0.359
0.283
0.340
0.698
0.530
0.353
0.363
0.402
0.373
0.363
0.369
0.309
0.357
ET1ml
192
0.332
0.374
0.314
0.360
0.744
0.555
0.376
0.380
0.510
0,435
0.417
0.405
0.346
0.381
336
0.353
0.393
0.338
0.377
0.801
0.582
0.399
0.395
0.590
0.477
0.447
0.428
0.373
0.408
720
0.388
0,386
0.374
0.403
0.829
0.606
0.432
0.417
0.703
0.525
0.513
0.470
0.475
0.477
avg
0.345
0.378
0.327
0.370
0.768
0.568
0.390
0.389
0.551
0.453
0.435
0.418
0.376
0.406
96
0.166
0.260
0.165
0.256
0.225
0.300
0.189
0.260
0.192
0.263
0.206
0.267
0.197
0.286
ETTm2
192
0.222
0,300
0.221
0,297
0.286
0.339
0.247
0.300
0.256
0.308
0.293
0.320
0.250
0.322
336
0.267
0.333
0.269
0.331
0.335
0.369
0.295
0.334
0.315
0.346
0.411
0.414
0.337
0.375
720
0.340
0.378
0.331
0.379
0,414
0.416
0.372
0.386
0.409
0.405
0.478
0.437
0.475
0.477
avg
0.249
0.318
0.247
0,316
0.315
0.356
0.276
0.320
0.293
0.331
0.347
0.360
0.315
0.365
0.359
0.390
0.344
0,380
0,454
0.434
0.380
0.398
0.389
0.409
0.421
0.401
0.350
0.382
ETThl
192
0.390
0:409
0.376
0.404
0.522
0.465
0.440
0.434
0.502
0.443
0.472
0.432
0.388
0.412
336
0.420
0,436
0,407
0.432
0.559
0.484
0.514
0.474
0.580
0.460
0.510
0.455
0.411
0,430
720
0.437
0.460
0.427
0.458
0.714
0.549
0.705
0.568
0.605
0.495
0.514
0.481
0.427
0.455
avg
0.401
0.424
0.388
0.419
0,562
0.483
0.510
0.469
0.519
0.452
0.479
0.442
0.394
0.420
0.278
0.342
0,279
0.340
0.316
0.359
0.287
0.325
0.306
0.338
0.326
0.355
0.302
0.354
ETTh2
192
0.345
0.383
0.335
0,383
0.374
0.398
0.347
0.367
0.396
0.394
0.397
0,400
0.364
0.385
336
0.394
0.416
0.366
0.410
0.381
0.410
0.377
0.393
0.423
0.417
0.431
0.413
0.417
0.425
720
0.430
0.445
0.413
0.445
0.408
0.434
0.404
0.421
0.442
0.439
0.446
0.444
0.527
0.496
avg
0.362
0.397
0.348
0.395
0,370
0.400
0.354
0.377
0.392
0.397
0.400
0,403
0,403
0.415
0.525
0,356
0.463
0.331
0.526
0.368
0.562
0.378
Traffic
192
0,547
0,365
0,504
0,353
0,561
0.385
0.579
0,412
336
0.645
0.419
0.593
0.401
0.614
0.412
0.594
0.420
720
0.722
0.457
0.685
0.440
0.749
0.464
0.723
0.472
avg
0.610
0.399
0,561
0.381
0.613
0.407
0.615
0.421
0.151
0.211
0.141
0.195
0.190
0.236
0.177
0.208
0.186
0.208
0.159
0.213
Weather
192
0.191
0.248
0,180
0.235
0.261
0.293
0.219
0.249
0.238
0.258
0.215
0.266
336
0.236
0.284
0.224
0.272
0.332
0.340
0.277
0.292
0.313
0.353
0.291
0.322
720
0.299
0.323
0.286
0.320
0.385
0.381
0.365
0.350
0.416
0.415
0.415
0.400
avg
0.219
0,266
0.208
0,256
0.292
0,313
0.260
0.275
0.288
0.309
0.270
0.300
96
0.084
0.203
0.085
0.204
0.095
0.219
0.096
0.213
0.099
0.219
0.096
0.215
0.145
0.267
Exchange
192
0.171
0.294
0.1
0.295
0.198
0.322
0.197
0,312
0.194
0.314
0.195
0.313
0.333
0.397
336
0.310
0.402
0.311
0.403
0.349
0.431
0.349
0.425
0.341
0.423
0.332
0.416
0.367
0.439
720
0.816
0.680
0.820
0.682
0.927
0.729
0.903
0.717
0.846
0.690
0.935
0.723
0.882
0.712
avg
0.345
0.395
0.347
0.396
0.392
0.425
0.386
0.417
0.370
0.412
0.390
0.417
0.432
0.454
96
0.209
0.309
0.181
0.263
0.591
0.504
0.682
0.688
0.373
0.304
0.408
0.345
0.304
0.345
192
0.220
0.315
0.190
0.270
0.689
0.567
0.694
0.695
0.363
0.303
0.466
0.373
0.309
0.342
Solar
336
0.228
0.314
0.197
0.277
0.831
0.636
0.719
0.706
0.391
0.319
0.526
0.407
0.433
0.450
720
0.218
0.283
0.198
0.274
0.972
0.710
0.759
0.725
0.444
0.349
0.601
0.461
0.599
0.576
avg
0.219
0.305
0.191
0.271
0.771
0.604
0.714
0.704
0.393
0.319
0.500
0.397
0.411
0.428
96
0.181
0.272
0.156
0.255
0.210
0.312
0.152
0.242
Electricity
192
0.195
0.284
0.183
0.282
0.239
0.337
0.171
0.259
336
0.253
0.338
0.240
0.338
0.284
0.372
0.192
0.278
720
0.304
0.382
0.275
0.357
0.456
0.479
0.236
0.313
avg
0.233
0.319
0.213
0.308
0.297
0.375
0.188
0.273
1st Count
7
31
25
0
0
7
10
0
0
0
0
2
16

---

LightGTS: A Lightweight General Time Series Forecasting Model
Table 13. The results of LightGTS- in zero-shot and full-shot setting and other baselines in full-shot setting. Lower MSE or MAE values indicate better predictions. Red: the best, Blue: the 2nd best.
LightGTS
LightGTTS
Models
PDF
ilrrnsformer
Pathformer
FITS
TimeMixer
PatchTST
(zcro-shot)
(full-shot)
Metric
MSB
MAE
MSE
MAR
MSE
MAF
MSB
MAB
MSE
MAR
MSE
MAE
MSE
MAE
MSB
MAE
96
0,283
0.340
0.266
0.320
0.286
0.340
0.287
0.342
0.290
0.335
0.303
0.345
0.293
0.345
0.289
0.343
ETTm!
192
0.314
0,360
0.307
0,349
0.321
0.364
0.331
0.371
0.337
0,363
0.337
0.365
0.335
0.372
0.329
0.368
336
0.338
0.377
0.334
0.370
0.354
0,383
0.358
0.384
0.374
0.384
0.368
0.384
0.368
0.386
0.362
0.390
720
0.374
0.403
0.377
0.405
0.408
0.415
0.412
0.416
0.428
0.416
0.420
0.413
0.426
0.417
0.416
0.423
avg
0,327
0,370
0.321
0.361
0.342
0.376
0.347
0.378
0,357
0,375
0.357
0,377
0.356
0.380
0.349
0.381
96
0.165
0,256
0.153
0.241
0.163
0.251
0.168
0.262
0.164
0.250
0,165
0.254
0.165
0.256
0.165
0.255
E77m2
192
0.221
0.297
0.209
0.286
0.219
0,290
0.224
0.295
0.219
0.288
0,219
0.291
0.225
0.298
0.221
0.293
336
0.269
0.331
0.259
0.318
0,269
0,330
0.274
0.330
0.267
0.319
0.272
0,326
0.277
0.332
0.276
0.327
720
0.331
0.379
0.336
0.367
0,349
0,382
0.367
0,385
0.361
0.377
0.359
0,381
0.360
0.387
0.362
0.381
aog
0.247
0.316
0.239
0,303
0,250
0,313
0.258
0.318
0.253
0.309
0.254
0.313
0.257
0.318
0.256
0.314
96
0.344
0,380
0.340
0.375
0,360
0.391
0,386
0.405
0,372
0,392
0.376
0,396
0,372
0.401
0.377
0.397
E1Th1
192
0.376
0.404
0.373
0.401
0.392
0.414
0.430
0.435
0.408
0.415
0,400
0.418
0.413
0.430
0.409
0.425
336
0.407
0.432
0.404
0.420
0,418
0.435
0.450
0,452
0,438
0.434
0.419
0.435
0.438
0.450
0.431
0.444
720
0.427
0.458
0.435
0.456
0,456
0.462
0.495
0.487
0.450
0.463
0.435
0.458
0.483
0.483
0.457
0.477
avg
0,388
0.419
0.388
0.413
0.407
0.426
0.440
0.445
0.417
0.426
0.408
0.427
0.427
0.441
0.419
0.436
96
0.279
0.340
0.268
0.326
0,276
0,341
0,292
0.347
0.279
0.336
0.277
0.345
0.270
0,342
0.274
0.337
E7Th2
192
0.335
0.383
0.333
0.369
0,339
0.382
0.348
0.384
0.345
0,380
0,331
0.379
0.349
0.387
0.348
0.384
336
0.366
0.410
0.353
0.390
0.374
0.406
0.372
0.407
0.378
0.408
0.350
0.396
0.367
0.410
0.377
0.416
720
0.413
0.445
0,385
0,425
0.398
0,433
0.424
0.444
0.437
0.455
0.382
0.425
0.401
0.436
0.406
0.441
avg
0.348
0.395
0.335
0.377
0.347
0.391
0.359
0.396
0.360
0.395
0.335
0.386
0.347
0.394
0.351
0.395
96
0.463
0.331
0.359
0.244
0.368
0,252
0.363
0.265
0.384
0.250
0.400
0,280
0.369
0,256
0.370
0.262
Traffic
192
0.504
0.353
0.382
0.250
0.382
0,26
0.384
0.273
0,405
0.257
0.412
0.288
0.400
0.271
0.386
0.269
336
0.593
0.401
0.395
0.262
0,393
0.268
0.396
0.277
0.424
0.265
0.426
0.301
0.407
0.272
0.396
0.275
720
0.685
0.440
0.435
0.279
0.438
0.297
0.445
0.308
0.452
0.283
0.478
0.339
0.462
0.316
0.435
0.295
avg
0.561
0.381
0,393
0.259
0,395
0.270
0.397
0.281
0,416
0.264
0.429
0,302
0.410
0.279
0.397
0.275
96
0.141
0.195
0,139
0.182
0.147
0.196
0.157
0.207
0.148
0.195
0.172
0.225
0.147
0.198
0.149
0.196
Weateer
192
0.180
0.235
0.180
0.224
0.193
0.240
0.200
0.248
0.191
0.235
0.215
0.261
0.191
0.242
0.191
0.239
336
0.224
0.272
0.225
0.262
0.245
0,280
0.252
0.287
0.243
0.274
0.261
0.295
0.244
0.280
0.242
0.279
720
0,286
0.320
0.284
0.309
0.323
0.334
0.320
0.336
0.318
0.326
0.326
0.341
0.316
0.331
0.312
0.330
avg
0,208
0,256
0.207
0.244
0,227
0,263
0.232
0.270
0.225
0.258
0.244
0.281
0.225
0.263
0.224
0,261
96
0.085
0,204
0.079
0.197
0,083
0,200
0.080
0.201
0.088
0.208
0.082
0.199
0.087
0.209
0.079
0,200
Exchange
192
0.172
0.295
0.162
0.290
0.172
0.294
0.155
0.287
0.183
0.304
0.173
0.295
0.178
0.300
0.159
0.289
336
0
0.403
0.295
0.395
0,323
0.411
0.298
0.399
0.354
0.429
0.317
0.406
0.376
0.451
0,297
0,399
720
0.820
0.682
0.750
0.650
0.820
0.682
0.749
0.650
0.909
0.716
0.825
0.684
0.897
0.711
0.751
0.650
avg
0.347
0.396
0.322
0,383
0,350
0.397
0.321
0.384
0.384
0.414
0.349
0.396
0.385
0.418
0.322
0.385
96
0.181
0,263
0.160
0.206
0,181
0,247
0.174
0,229
0.218
0.235
0.208
0.255
0.180
0.233
0,170
0.234
Solar
192
0.190
0.270
0.180
0.219
0,200
0.259
0.205
0.270
0.196
0.220
0.229
0.267
0.201
0.259
0.204
0.302
336
0.197
0.277
0.188
0.220
0,208
0.269
0.216
0.282
0.195
0.220
0.241
0.273
0.214
0.272
0.212
0.293
720
0,198
0.274
0.190
0.234
0,212
0.275
0,211
0.260
0.208
0.237
0.248
0.277
0.218
0.278
0.215
0.307
avg
0.191
0.271
0.179
0.220
0.200
0.263
0.202
0.260
0.204
0.228
0.232
0.268
0.203
0.261
0.200
0.284
96
0.156
0.255
0.124
0.216
0.128
0.222
0.134
0.230
0.135
0.222
0.139
0.237
0.153
0.256
0.143
0.247
Electricity
192
0.183
0.282
0.145
0.240
0.147
0.242
0.154
0.250
0.157
0.253
0.154
0.250
0.168
0,269
0.158
0,260
336
0.240
0.338
0.163
0.252
0.165
0.260
0.169
0.265
0.170
0.267
0.170
0.268
0.189
0.291
0.168
0.267
720
0.275
0.357
0.191
0.282
0.199
0.289
0.194
0.288
0.211
0.302
0.212
0.304
0.228
0.320
0.214
0.307
avg
0.213
0.308
0.156
0.248
0.160
0.253
0.163
0.258
0.168
0.261
0.169
0.265
0.185
0.284
0.171
0.270
1st Count
5.
1
31
42
0
0
3
0
0
17

---

LightGTS: A Lightweight General Time Series Forecasting Model
Table 14. Ablations key components of LightGTS in zero-shot setting, including periodical tokenization, and periodical parallel decoing.
Decoding
Periodical Parallel Decoding
Autoregressive Decoding
Masked Autoencoder
Tokenization
Periodical
Fixed
Periodical
Fixed
Periodical
Fixed
Metric
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
96
0.283
0.340
0.658
0.509
0.320
0.368
0.623
0.499
0.351
0.385
0.768
0.572
ETTml
192
0.314
0.360
0.667
0.523
0.342
0.381
0.659
0.515
0.371
0.397
0.792
0.593
336
0.338
0.377
0.686
0.541
0.361
0.394
0.704
0.544
0,387
0,411
0,808
0,603
720
0.374
0.403
0.704
0.559
0.390
0.414
0.734
0.565
0.448
0.457
0.852
0.627
avg
0.327
0.370
0.679
0.533
0.353
0.389
0.680
0.531
0.389
0,412
0.805
0,599
96
0.165
0.256
0.210
0.297
0.169
0.260
0.208
0.294
0,202
0,291
0.308
0.356
E11m2
192
0.221
0.297
0.276
0.335
0.226
0.300
0.280
0.339
0.259
0.328
0.391
0.404
336
0.269
0.331
0.336
0.369
0.272
0.335
0.346
0.380
0.293
0.355
0.423
0.425
720
0.331
0.379
0.433
0.423
0.331
0.380
0.444
0.436
0.379
0.420
0.492
0.466
avg
0.247
0.316
0.314
0.356
0.250
0.319
0.320
0.362
0.283
0.349
0.404
0.413
96
0.344
0.380
0.364
0.396
0.365
0.397
0.365
0.397
0.401
0.423
0.393
0.415
192
0.376
0.404
0.391
0.413
0.392
0.415
0.392
0.415
0,433
0,449
0.452
0,459
ETThl
336
0.407
0.432
0.409
0.430
0,401
0.427
0.411
0.436
0.444
0.463
0.532
0,513
720
0.427
0.458
0.421
0.451
0.420
0.453
0.432
0.453
0.534
0.529
0.623
0.572
avg
0,388
0.419
0.396
0.423
0.394
0.423
0.400
0.425
0.453
0.466
0,500
0.490
96
0.279
0.340
0.283
0,346
0,279
0,341
0.285
0.344
0.307
0.368
0.378
0.411
192
0.335
0.383
0.339
0.385
0.339
0.384
0.342
0.387
0.383
0.423
0.454
0.461
ETTh2
336
0.366
0.410
0.382
0.413
0.386
0.419
0.385
0.419
0,464
0.463
0.463
0,470
720
0.413
0.445
0,412
0.438
0.463
0.469
0.455
0.465
0,550
0,517
0.465
0.477
avg
0.348
0.395
0.354
0.396
0.367
0.403
0.367
0.404
0.426
0.443
0.440
0.455
0.141
0.195
0.164
0.210
0.154
0.211
0.164
0.211
0.188
0.249
0,239
0,281
192
0.180
0.235
0.219
0.261
0.194
0.248
0.219
0.266
0,227
0.278
0.319
0.333
Weather
336
0.224
0.272
0.282
0.308
0.244
0.286
0.285
0.315
0.273
0.309
0.359
0.363
720
0.286
0.320
0.381
0.371
0.314
0.336
0.392
0.379
0.351
0.368
0.437
0.417
avg
0.208
0.256
0.262
0.288
0.226
0.270
0.265
0.293
0.260
0.301
0.339
0.349
96
0.156
0.255
0.192
0.287
0.197
0.287
0.199
0.297
0.245
0.321
0.207
0.299
Electricity
192
0.183
0.282
0.205
0.297
0.210
0.303
0.212
0.307
0.277
0.355
0.263
0.357
336
0.240
0.338
0.231
0.320
0.233
0.326
0.236
0.327
0.318
0.395
0.396
0,460
720
0.275
0.357
0.275
0.355
0.276
0,361
0.279
0.372
0.450
0.495
0.623
0,597
avg
0.213
0.308
0.226
0.315
0.229
0.319
0.231
0.326
0.322
0.392
0.372
0.428
96
0.463
0.331
0.579
0.383
0.603
0.392
0.592
0.394
0.656
0.425
0.607
0,402
192
0.504
0.353
0.591
0.389
0.612
0,402
0.600
0.396
0.690
0.453
0.686
0.470
Traffic
336
0.593
0.401
0.630
0.407
0.639
0.408
0.641
0.417
0.740
0.487
0.874
0.586
720
0.685
0.440
0.686
0.433
0.682
0.440
0.686
0.438
0.900
0.571
1.044
0.679
0.561
0.381
0.621
0.403
0.634
0.410
0.630
0.411
0.746
0.484
0.803
0.534
96
0.181
0.263
0.222
0.304
0.190
0.270
0.212
0.308
0.205
0.290
0.464
0.490
192
0.190
0.270
0.345
0.371
0.207
0.282
0.368
0.385
0.213
0.294
0.508
0.504
Solar
336
0.197
0.277
0,400
0.423
0.211
0.287
0.446
0.468
0.217
0.300
0.561
0.532
720
0.198
0.274
0.529
0.542
0.215
0.296
0.535
0.505
0.235
0.330
0.724
0.645
avg
0.191
0.271
0.374
0.410
0.206
0.284
0.390
0.417
0.217
0.304
0.564
0.543
18


Reviews:
[{"review_id": "TsrDh5sVBg", "reviewer": "Reviewer_3dom", "summary": "The paper proposes a general purpose pretrained time series forecasting model called LightGTS. The model is an encoder-decoder transformer operating on patches of time series observations. However, unlike existing works which operate on fixed patch lengths, LightGTS uses a dynamically adjusted patch length which is aligned to the seasonality of the time series. Authors argue that this enables better modeling of time series data compared to an arbitrarily selected fixed patch length. Empirical results have been reported on 9 time series datasets.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: Improve the quality of evaluation**\n\nA1: We use Chronos Benchmark II you mentioned to further evaluate the generalizability of LightGTS. As shown in the table below, LightGTS shows outstanding performance, second only to Moirai-large whose training corpus overlap is much higher. In addition, LightGTS also exhibits superior efficiency compared to other foundation model. \n\n| Model | Moirai-large | Chronos-large | TimesFM | LightGTS_mini(ours) | Seasonal Naive |\n| --- | --- | --- | --- | --- | --- |\n| Average Relative Error | **0.791** | 0.824 | 0.882 | 0.819 | 1.000 |\n| Median inference time (s) | 14.254 | 26.827 | 0.396 | 1.390 | **0.096** |\n| Training corpus overlap (%) | 81.5% | 0% | 14.8% | 31% | 0% |\n\n**Q2: Periodical Patching vs. Multi-Patching**\n\nA2:  While MOIRAI's predefined patch sizes based on sampling frequency offer some solution for  consistent modeling across different frequencies, they are still fixed and lack flexibility in certain scenarios. In contrast, Periodical Patching adaptively divides patches according to scale-invariant periodicity, enabling more flexible and unified modeling for datasets with varying frequencies.\n\n**Q3: Some works such as TinyTimeMixers have made similar claims as LightGTS and should be discussed as part of related work.**\n\nA3: Thank you for mentioning TTMs, which are also lightweight TSFMs like LightGTS. We will differentiate LightGTS from TTMs in the following two aspects:\n\n- **Flexibility**: TTMs have fixed input and output formats, which imposes limitations in downstream applications. In contrast, LightGTS supports flexible input and output configurations.\n- **Adaptive Patching**: While TTMs employ adaptive patching through CV-inspired patch merging techniques to capture multi-scale features, they remain constrained by predefined patch sizes. LightGTS, however, leverages periodical patching that adaptively segments time series based on the intrinsic periods. This approach enables LightGTS to achieve unified modeling across datasets with varying scales.\n\nWe would update it in the related work of the revised paper.\n\n**Q4: LightGTS is only a point forecaster, whereas most existing pretrained models (Chronos, Moirai, TimesFM, Chronos-Bolt) support probabilistic forecasting. Uncertainty quantification is critical feature for downstream decision making based on a forecast.**\n\nA4: We are developing an enhanced version of LightGTS with quantile regression pre-train task to support probabilistic forecasting (**uncertainty quantification**), which will be released in future updates.\n\n**Q5: Replace non-standard terms (e.g., \"scale\" for frequency, \"cycle length\" for seasonality) with established conventions.** \n\nA5:  We sincerely appreciate your feedback regarding terminology alignment. In the revised manuscript, we will systematically replace non-standard terms with established terminology from time series. \n\n**Q6: Was the model only trained on the ETTh1 dataset? How does the model perform quantitatively when trained on a single seasonality?Why does the pretraining corpus include diverse seasonalities, and how were they selected?**\n\nA6: \n\n- Yes, we found that pre-training on a single seasonality dataset can enable effective transfer learning.\n- **Experiment:** LightGTS-single was pre-trained on ETTh1 and directly tested on downstream datasets in a zero-shot setting. As shown in the table below, LightGTS-single achieved strong transfer performance on datasets with single seasonality (e.g., Solar), while its performance was less optimal on datasets with multiple seasonalities (e.g., Electricity). By pre-training on multi-seasonalities datasets, LightGTS-mini significantly improved its performance on datasets with multiple seasonalities.\n\n| Datasets | ETTh2 | ETTm2 | Weather | Solar | Electricity |\n| --- | --- | --- | --- | --- | --- |\n| Metrics | MSE/MAE | MSE/MAE | MSE/MAE | MSE/MAE | MSE/MAE |\n| PatchTST | 0.351/0.395 | 0.256/0.314 | 0.224/0.261 | 0.200/0.284 | 0.171/0.270 |\n| LightGTS-single | 0.357/0.381 | 0.251/0.314 | 0.232/0.274 | 0.227/302 | 0.246/0.358 |\n| LightGTS-mini | 0.359/0.396 | 0.250/0.318 | 0.210/0.258 | 0.196/0.269 | 0.214/0.306 |\n- **Pre-training corpus selection:** We did not explicitly filter datasets based on seasonality. Instead, we collected datasets from diverse domains (e.g., energy, weather, traffic), assuming that time-series data from different domains inherently contain distinct seasonal patterns. This approach ensures broader generalizability while retaining domain-specific characteristics.", "claims_and_evidence": "The central claim of the paper is that LightGTS is a general purpose pretrained time series model which is more accurate and lightweight compared to existing pretrained models. Authors argue that \"existing TSFMs largely depends on massive pre-training data and large model parameters\". \n\n**Existing models depend on large scale training and large number of parameters**: Although this is true for most existing models, in the end, LightGTS is also pretrained on a large scale multi-source corpus. However, the claim about fewer number of parameters is correct.\n\n**LightGTS is more accurate compared to existing TSFMs**: This claim is not supported by the evaluation conducted in the paper. In particular, the evaluation is severely limited to draw meaningful conclusions. The experiment design also suffers from serious flaws that have previously been discussed in the community. Note that these flaws are not unique to LightGTS and have also existed in previous works. However, with the rapid progress in the field and existence of better benchmarks, it is imperative that newer works do a better job at evaluation, especially when the claim involves a general purpose pretrained model. Please see **Methods And Evaluation Criteria** for details. \n\n**Fixed patch embedding does not transfer well to new seasonalities**: The experiment in Fig 2 demonstrates this to a certain degree and I intuitively agree with this assertion. However, more evidence is needed showing that this is an issue in existing patch-based pretrained models such as Chronos-Bolt and TimesFM. I also have questions about Fig 2. Please refer to **Questions for Authors**.", "methods_and_evaluation_criteria": "The authors propose a reasonable architecture for a general purpose time series model. I particularly find the contribution of periodical patching quite interesting. I would encourage the authors to set the stage better for their approach, e.g., by discussing Moirai better. Moirai uses multiple patch sizes and a patch selection mechanism with a similar motivation to LightGTS. Periodical patching is a natural and elegant way to address the limitation of fixed patch sizes.\n\nThe breadth of experiments is severely limited for a general purpose model. Only 9 datasets have been studied, which is not enough to justify the title of a general purpose model. Moreover, 5 of these datasets belong to the same domain with 4 being essentially the same dataset (ETTh1, ETTh2, ETTm1, ETTm2). This infamous \"ETT long term forecasting benchmark\" is often criticized for its flaws such as limited domain coverage and the practice of forecasting at unreasonable horizons (e.g., 720 days into the future for exchange rate or oil temperature of a transformer at a specific hour months into the future). Every new model somehow beats this benchmark; however, there is still barely any absolute progress, only an illusion of it. Please refer to the talk (and paper) from Christoph Bergmeir [1, 2] where he discusses the limitation of this benchmark and current evaluation practices. A _very recent_ position paper [3] also conducted a comprehensive evaluation of models on this benchmark showing that there's no obvious winner. \n\nOne (not so difficult) way to improve the quality of evaluation is to include results on better benchmarks that have been proposed recently in the context of pretrained time series models. \n\n- Chronos Benchmark II: This benchmark includes 27 datasets (42, if you include Benchmark I) providing a comprehensive coverage over domains, frequencies and other properties. Please refer to https://github.com/autogluon/fev for details on how to use the benchmark.\n- GIFT-Eval: This benchmark includes 90+ tasks across multiple datasets and domains. It also provides a leaderboard of existing pretrained models. Please refer to https://github.com/SalesforceAIResearch/gift-eval. \n\n[1] https://neurips.cc/virtual/2024/workshop/84712#collapse108471      \n[2] Hewamalage, Hansika, Klaus Ackermann, and Christoph Bergmeir. \"Forecast evaluation for data scientists: common pitfalls and best practices.\" Data Mining and Knowledge Discovery 37.2 (2023): 788-832.                   \n[2] Brigato, Lorenzo, et al. \"Position: There are no Champions in Long-Term Time Series Forecasting.\" arXiv preprint arXiv:2502.14045 (2025).", "theoretical_claims": "The paper does not make theoretical contributions. Also, **Theorem 3.1** is not a theorem per se but more of a remark.", "experimental_designs_or_analyses": "Please see **Methods and Evaluation Criteria**.", "relation_to_broader_scientific_literature": "The paper makes a contribution to the rapidly evolving area of pretrained time series forecasting models. The idea of periodical patching is promising and addresses the issue of fixed patch sizes in previous models. The evaluation is limited and can be improved by the inclusion of better benchmarks.", "essential_references_not_discussed": "Some works such as TinyTimeMixers have made similar claims as LightGTS and should be discussed as part of related work.", "other_strengths_and_weaknesses": "LightGTS is only a point forecaster, whereas most existing pretrained models (Chronos, Moirai, TimesFM, Chronos-Bolt) support probabilistic forecasting. Uncertainty quantification is critical feature for downstream decision making based on a forecast.", "other_comments_or_suggestions": "Authors use new terms for known quantities in time series forecasting. For example, _scale_ is used to refer to _frequency_ and _cycle length_ is used to refer to _seasonality_. I would encourage the authors to use existing terms to better align with the literature.", "questions_for_authors": "- For the experiment in Fig 2, did the authors only trained the model on ETTh1 dataset? If yes, I find it very surprising that it transfers to very different types of seasonal patterns such as those in the solar dataset. Is the claim here that only pretraining on a single seasonality could somehow deliver a pretrained model? Out of curiosity, how does the model only trained with a single seasonality perform quantitatively? Why does the pretraining corpus contain diverse seasonalities and how were these selected?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "x9ig8Sq8Se", "reviewer": "Reviewer_AuKx", "summary": "In this paper, the authors proposed a lightweight pretrained TSF model with a new tokenization technique. With the proposed periodical tokenization method, the authors claimed that one can naturally deal with time series with different granularity and periodicity. In addition, it significantly reduced the number of model parameters for pretraining, while achieving SOTA performance on one benchmark dataset.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: Larger benchmark datasets should be used for evaluating the pretrained TSF model.**\n\nA1: We use Chronos Benchmark II to further evaluate the effectiveness of LightGTS. As shown in the table below, LightGTS shows outstanding performance, second only to Moirai-large whose training corpus overlap is much higher. In addition, LightGTS also exhibits superior efficiency compared to other foundation model. \n\n| Model | Moirai-large | Chronos-large | TimesFM | LightGTS_mini(ours) | Seasonal Naive |\n| --- | --- | --- | --- | --- | --- |\n| Average Relative Error | **0.791** | 0.824 | 0.882 | 0.819 | 1.000 |\n| Median inference time (s) | 14.254 | 26.827 | 0.396 | 1.390 | **0.096** |\n| Training corpus overlap (%) | 81.5% | 0% | 14.8% | 31% | 0% |\n\n**Q2: Light-weight time series models [1] [2] or even non-parametric models [3] that use periodical information to improve forecasting should be discussed.**\n\nA2: \n\n- CycleNet, SparseTSF, and OneShotSTL all propose explicit periodicity decomposition methods to enhance the accuracy and lightweight nature of time series forecasting models. However, LightGTS not only explicitly models periodicity through periodic patching but also adapts to multivariate time series pretraining via flex resizing technique. This allows the model to leverage the scale-invariant periodicity inductive bias in multivariate time series, achieving strong zero-shot performance with fewer parameters.\n- Experiment (MSE)：\n\n| Datasets | LightGTS_mini | SparseTSF | CycleNet | OneShotSTL |\n| --- | --- | --- | --- | --- |\n| ETTm2 | **0.239** | 0.251 | 0.244 | 0.255 |\n| Electricity | **0.156** | 0.162 | 0.159 | 0.167 |\n| Traffic | **0.393** | 0.404 | 0.397 | 0.403 |\n\n**Q3: Specific experimental settings should be given. For instance, which period is used for training and evaluation? How long is the context length?**\n\nA3: \n\n- For datasets with prior knowledge of period, we use known period. For datasets where the period is not known, we use Fast Fourier Transform (FFT) to extract the period.\n- We use a variable context length, keeping the number of tokens at 10. For example, for a dataset with a period of 24, we set the context length to 240.\n\n**Q4: How would the proposed model perform trend forecasting? Does it go back to point patch? Then the model size would be significantly affected, if there are many non-periodic time series in the pretraining datasets, right? Emperically, how does the proposed model perform on such datasets?**\n\nA4: Actually, for datasets with little periodicity, LightGTS is insensitive to the prediction of trends with the selection of patch size, and the the model size would be affected by the selection of patch size. Take the exchange dataset which exhibits little periodicity as an example, the performance of LightGTS in zero-shot setting remains stable when the patch size is set to 1, 4, 6, 8, 16 and 24, respectively. In the paper, we use fft-extracted periods: 6.\n\n| Patch size | 1(**point patch**) | 4 | 6 (fft-extracted) | 8 | 16 | 24 |\n| --- | --- | --- | --- | --- | --- | --- |\n| Exchange-MSE | 0.347 | 0.348 | 0.347 | 0.353 | 0.351 | 0.354 |\n\n**Q5: How to deal with different cycle lengths.** \n\nA5: For the case where a time series is known to have different cycle lengths, we pick the smallest cycle as the patch size. For example, traffic and electricity dataset both have two cycle lengths, 24 (one day) and 168 (one week), and we choose 24 as the patch size. For the case where the cycle length is not well known, FFT can be used for cycle length extraction, which we have discussed in the Appendix B.1.", "claims_and_evidence": "No, the authors claimed that they proposed a general time series forecasting model. However, the proposed periodical patching and periodical parallel decoding, the core component of the proposed LightGTS, are only designed for periodical time series data. In addition, they only evaluate datasets with strong periodic (long-term TSF benchmark). Therefore, it is not clear how the proposed method performs on non-periodic time series, which are prevalent in the real world as well. Therefore, in my opinion, it is not appropriate to claim the statement of the general TSF model.", "methods_and_evaluation_criteria": "They only evaluated datasets with strong periodic (long-term TSF benchmark). Larger benchmark datasets should be used for evaluating the pretrained TSF model, e.g., GIFT-Eval.", "theoretical_claims": "No, there are no theoretical claims in the paper.", "experimental_designs_or_analyses": "The choice of evaluation datasets should be improved.\nThe experimental settings are incomplete.", "relation_to_broader_scientific_literature": "The proposed a new tokenization method for time series datasets utilizing periodical information. The idea seems to be novel and technically sounds.", "essential_references_not_discussed": "Light-weight time series models [1] [2] or even non-parametric models [3] that use periodical information to improve forecasting should be discussed.\n[1] Lin, S., Lin, W., Wu, W., Chen, H., & Yang, J. (2024). Sparsetsf: Modeling long-term time series forecasting with 1k parameters. arXiv preprint arXiv:2405.00946.\n[2] Lin, S., Lin, W., Hu, X., Wu, W., Mo, R., & Zhong, H. (2024). Cyclenet: enhancing time series forecasting through modeling periodic patterns. Advances in Neural Information Processing Systems, 37, 106315-106345.\n[3] He, X. Li, Y., Tan, J., Wu B. & Li, F. (2023).  OneShotSTL: One-Shot Seasonal-Trend Decomposition For Online Time Series Anomaly Detection And Forecasting. VLDB Endowment, 16, 06, 1399-1412.", "other_strengths_and_weaknesses": "Strengths:\n1. The proposed periodical patching and projection layer looks novel and interesting. It seems to be a good way to handle datasets with different gradualility and periodicity.\n\nWeeknesses\n1. How the method would handle periodic and non-periodic datasets together is not clear.\n2. Again, the evaluation datasets are not enough.\n3. Specific experimental settings should be given. For instance, which period is used for training and evaluation? How long is the context length?\n4. Some related works are missing.", "other_comments_or_suggestions": "Page 1, line 12, pertaining -> pretraining", "questions_for_authors": "1. How would the proposed model perform trend forecasting? Does it go back to point patch? Then the model size would be significantly affected, if there are many non-periodic time series in the pretraining datasets, right? Emperically, how does the proposed model perform on such datasets?\n2. How would the proposed method deal with different cycle lengths? For instance, there are daily and weekly periods in traffic data. How did the authors pick them?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "o9inoylqsY", "reviewer": "Reviewer_CW8j", "summary": "The paper introduces LightGTS, a lightweight time series forecasting model leveraging consistent periodical modeling. It proposes a periodical tokenization, which adaptively splits time series into patches aligned with intrinsic periods to handle varying scales, and periodical parallel decoding, which leverages historical tokens to improve forecasting while avoiding autoregressive errors. Experments show that LightGTS achieves SOTA performance on 9 benchmarks in zero/full-shot settings with <5M parameters, significantly improving efficiency over existing foundation models.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: The zero-shot evaluation requires further validation for generalizability to unseen scales and periods, such as an ablation study on cycle-length estimation.**\n\nA1: To further evaluate the generalizability of LightGTS, we add experiments on Chronos Benchmark II which contains 27 evaluation datasets with different scales and periods. As shown in the table below, LightGTS shows outstanding performance, second only to Moirai-large whose training corpus overlap is much higher. In addition, LightGTS also exhibits superior efficiency compared to other foundation model. \n\n| Model | Moirai-large | Chronos-large | TimesFM | LightGTS_mini(ours) | Seasonal Naive |\n| --- | --- | --- | --- | --- | --- |\n| Average Relative Error | **0.791** | 0.824 | 0.882 | 0.819 | 1.000 |\n| Median inference time (s) | 14.254 | 26.827 | 0.396 | 1.390 | **0.096** |\n| Training corpus overlap (%) | 81.5% | 0% | 14.8% | 31% | 0% |\n\n**Q2: Cycle-length detection ablation is unclear; limited discussion of failure modes (e.g., non-periodic series).**\n\nA2: Actually, for datasets with little periodicity, LightGTS is insensitive to the prediction of trends with the selection of patch size. Take the exchange dataset which exhibits little periodicity as an example, the performance of LightGTS in zero-shot setting remains stable when the patch size is set to 1, 4, 6, 8, 16 and 24, respectively. In the paper, we use fft-extracted period: 6.\n\n| Patch size | 1 | 4 | 6 (fft-extracted) | 8 | 16 | 24 |\n| --- | --- | --- | --- | --- | --- | --- |\n| Exchange-MSE | 0.347 | 0.348 | 0.347 | 0.353 | 0.351 | 0.354 |\n\n**Q3: Clarify the detection and effectiveness of intrinsic periods across datasets. The periods determined for datasets with unknown/noisy periodicities?**\n\nA3:  For datasets with prior knowledge of period, we use known period. For datasets where the period is not known, we use Fast Fourier Transform (FFT) to extract the period, which we have discussed in the Appendix B.1.\n\nIn Table 8, we give the cycle lengths of the evaluation dataset. For traffic and electricity dataset with two cycle lengths: 24 (one day) and 168 (one week), we choose the smaller cycle length 24 as the patch size. For the exchange dataset with insignificant periodicity, we use fft to extract the cycle length of 6.\n\nIn Table 4 of  paper, we perform an ablation study against periodical patching on seven datasets. After replacing periodical patching with a fixed patching, the model’s performance decreases significantly, validating the effectiveness of periodical patching.", "claims_and_evidence": "The claims regarding improved generalization and handling diverse scales through periodic tokenization are supported by case studies (e.g., Figure 2b) and multi-dataset benchmark experiments. However, the assumption of 'consistent periodic patterns' relies on accurately detecting intrinsic periods, yet the validation of this detection remains unclear. While the authors provide a comparison in Appendix Figure 6, the distinction between LightGTS and LightGTS-FFT is not well explained. Additionally, results indicate that the proposed method underperforms on strongly periodic data (e.g., Electricity) but excels when periodicity is less pronounced. This contradicts the claims and explanations in Appendix B.1.", "methods_and_evaluation_criteria": "Periodical tokenization aligns with time series' cyclical inductive bias, addressing fixed tokenization's limitations. Parallel decoding avoids error accumulation, a known issue in autoregressive models. Evaluation on 9 benchmarks is reasonable.", "theoretical_claims": "The author provides a brief theoretical analysis in Sec. 3.2, focusing on explaining the resize transformation of the projection layer weights.", "experimental_designs_or_analyses": "The experiments span diverse datasets with a well-reasoned design, including zero/full-shot settings and hyper-parameter studies. However, the zero-shot evaluation requires further validation for generalizability to unseen scales and periods, such as an ablation study on cycle-length estimation.", "relation_to_broader_scientific_literature": "LightGTS builds on time series foundation models by addressing fixed tokenization limitations. It aligns with recent trends in adaptive tokenization but uniquely integrates periodicity. The decoding approach relates to non-autoregressive methods in NLP/TSF, though periodicity integration is novel.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "Strengths: Novel integration of periodicity into tokenization/decoding, strong empirical results, and practical efficiency.  \n\nWeaknesses: Cycle-length detection ablation is unclear; limited discussion of failure modes (e.g., non-periodic series).", "other_comments_or_suggestions": "Clarify the detection and effectiveness of intrinsic periods across datasets.\n\n\n## update after rebuttal\nThe concerns raised have been addressed. I will maintain the original acceptance score.", "questions_for_authors": "Cycle detection: How are intrinsic periods determined for datasets with unknown/noisy periodicities?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "RGj01RkZOB", "reviewer": "Reviewer_Kj5L", "summary": "This paper presents LightGTS, a lightweight base model for time-series forecasting, along with Periodical Patch Embedding to adapt to intrinsic periodic differences across datasets and Periodical Parallel Decoding to prevent error accumulation. LightGTS achieves 10 to 100 times size reduction based only on 4 million parameters.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1: Discussions and experimental comparisons with Tiny Time Mixers (TTMs).**\n\nA1: Thank you for mentioning TTMs, which are also lightweight TSFMs like LightGTS. We will differentiate LightGTS from TTMs in the following two aspects:\n\n- **Flexibility**: TTMs have fixed input and output formats, which imposes limitations in downstream applications. In contrast, LightGTS supports flexible input and output configurations.\n- **Adaptive Patching**: While TTMs employ adaptive patching through CV-inspired patch merging techniques to capture multi-scale features, they remain constrained by predefined patch sizes. LightGTS, however, leverages periodical patching that adaptively segments time series based on the intrinsic periods. This approach enables LightGTS to achieve unified modeling across datasets with varying scales.\n\nBased on your suggestions, we add a comparison experiment with TTMs. The following table shows the average MSE in zero shot setting, and LightGTS outperforms TTMs on most datasets.\n\n| Model | ETTh1 | ETTh2 | ETTm1 | ETTm2 | weather | electricity |\n| --- | --- | --- | --- | --- | --- | --- |\n| LightGTS-mini | **0.388** | 0.348 | **0.327** | **0.247** | **0.208** | 0.213 |\n| TTMs-Advanced | 0.4 | **0.333** | 0.362 | 0.252 | 0.231 | **0.192** |\n\n**Q2: The article's expression and description need some revision.** \n\nA2: Thank you for your detailed suggestions, we will correct the errors you mentioned in the revised paper.\n\n**Q3: Need a diagram illustrating the differences between the Periodical Patching and Periodical Parallel Decoding techniques and traditional practices.** \n\nA3:  \n\n- As shown in Figure 2 (a), the key difference of Periodical Patching from other patching techniques is its ability to adaptively perform consistent modeling on multivariate time series datasets with varying scales.\n- The differences between Periodical Parallel Decoding and other decoding techniques are shown in the table below.\n\n\n| Decoding techniques | Flexible Input/Output | Hight Inference | Pre-train/Downstream Consistency |\n| --- | --- | --- | --- |\n| Auto-regressive Decoding | √ | X | √ |\n| MLP Decoding | X | √ | √ |\n| Masked Auto-encoders | √ | √ | X |\n| Periodical Parallel Decoding | √ | √ | √ |", "claims_and_evidence": "yes", "methods_and_evaluation_criteria": "yes", "theoretical_claims": "yes", "experimental_designs_or_analyses": "should add more similar works into comparsion", "relation_to_broader_scientific_literature": "the significant contribution of this paper is very similar to that of the article, which also puts forward an Adaptive patching technology. such as Tiny Time Mixers (TTMs)", "essential_references_not_discussed": "n/a", "other_strengths_and_weaknesses": "pros:\n\n1. The proposed techniques are plug-and-play and can be combined with many time series forecasting models.\n\n2.The model achieves very good performance despite its extremely lightweight design.\n\ncons:\n\n1. Although the idea of training a lightweight temporal foundation model is quite interesting, there have been some cutting-edge works that made similar attempts, such as Tiny Time Mixers (TTMs): Fast Pre-trained Models for Enhanced Zero/Few-Shot Forecasting of Multivariate Time Series. Moreover, the significant contribution of this paper is very similar to that of the article, which also puts forward an Adaptive patching technology. I think the authors should have more discussions with relevant literature and add corresponding experimental comparisons.\n\n2. The article's expression and description need some revision. Last word of the first sentence of the abstract should perhaps be 'pretraining' instead of 'pertaining'. It might be helpful to include a diagram illustrating the differences between the Periodical Patching and Periodical Parallel Decoding techniques and traditional practices. This will better help readers understand.", "other_comments_or_suggestions": "n/a", "questions_for_authors": "see concerns above", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: Contributions
[1] The paper presents LightGTS, a pre-training time-series forecasting model that works on variable patch lengths. The patch lengths are aligned to the seasonality of time-series. [Reviewer 3dom]
[2] Proposed a new tokenization method for time series datasets utilizing periodical information [Reviewer AuKx]
[3] It proposes a periodical tokenization, which adaptively splits time series into patches aligned with intrinsic periods to handle varying scales, and periodical parallel decoding [Reviewer CW8j]
[4] The significant contribution of this paper is very similar to that of the article, which also puts forward an Adaptive patching technology. such as Tiny Time Mixers (TTMs) [Reviewer Kj5L]

Weakness:
[1] The paper claims a foundation model with fewer parameters, and demonstrates that the fixed patch embedding does not transfer well to new seasonalities [Reviewer 3dom]
[2] To the comment of [Reviewer AuKx] that the paper only addresses periodic time-series data, authors have demonstrated the method on some non-periodic data sets during rebuttal and claim that “By computing the attention between patch tokens, the model also learns the overall trend of time series”. An ablation study to support the claim that  parallel decoding helps with trend forecasting is important.
[3] In response to [Reviewer Kj5L] comments on comparison with TTMs, author have made a comparative study with TTMs-advanced.
Decision: Accept (poster)