Zero-shot Forecasting by Simulation Alone
Authors: Boris N. Oreshkin
Mayank Jauhari
Ravi Kiran Selvam
Malcolm Wolff
Wenhao Pan
Shankar Ramasubramanian
Kin G. Olivares
Tatiana Konstantinova
Andres Potapczynski
Mengfei Cao
Dmitry Efimov
Michael W. Mahoney
Andrew Gordon Wilson
Venue: ICLR 2026 Poster (2026)
Keywords: forecasting
foundation models
simulation
zero-shot
Primary area: learning on time series and dynamical systems

Abstract: Zero-shot time-series forecasting holds great promise, but is still in its infancy, hindered by limited and biased data corpora, leakage-prone evaluation, and privacy and licensing constraints. Motivated by these challenges, we propose the first practical univariate time series simulation pipeline which is simultaneously fast enough for on-the-fly data generation and enables notable zero-shot forecasting performance on M-Series and GiftEval benchmarks that capture trend/seasonality/intermittency patterns, typical of industrial forecasting applications. Our simulator, which we call SarSim (SARIMA Simulator for Zero-Shot Forecasting), is based off of a seasonal autoregressive integrated moving average (SARIMA) model as its core data source. Due to instability in the autoregressive component, naive SARIMA simulation often leads to unusable paths. Instead, we follow a three-step procedure: (1) we sample well-behaved trajectories from its characteristic polynomial stability region; (2) we introduce a superposition scheme that combines multiple paths into rich multi-seasonality traces; and (3) we add rate-based heavy-tailed noise models to capture burstiness and intermittency alongside seasonalities and trends. SarSim is orders of magnitude faster than kernel-based generators, and it enables training on circa 1B unique purely simulated series, generated on the fly; after which well-established neural network backbones exhibit strong zero-shot generalization, surpassing strong statistical forecasters and recent foundation baselines, while operating under strict zero-shot protocol. Notably, on GiftEval we observe a "student-beats-teacher" effect: models trained on our simulations exceed the forecasting accuracy of the AutoARIMA generating processes.

Published as a conference paper at ICLR 2026
ZERO-SHOT FORECASTING BY SIMULATION ALONE
Boris N. Oreshkin', , Mayank Jauhari', Ravi Kiran Selvam', Malcolm Wolff', Wenhao Pan 1.2 Shankar Ramasubramanian" Kin G. Olivares', Tatiana Konstantinova', Andres Potapczynski 1.3 Mengfei Cao', Dmitry Efimov?, Michael W. Mahoney', Andrew G. Wilson 'Amazon Science University of Washington 3 New York University creshki n aaaazooonn com
ABSTRACT
Zero-shot time-series forecasting holds great promise, but is still in its infancy, hin- dered by limited and biased data corpora, tarkage-prone evaluation, and privacy and licensing constraints. Motivated by these challenges, we propose the first practical univariate time series simulation pipeline which is simultaneously fast enough for on-the-fly data generation and enables notable zero-shot forecasting performance on M-Series and GiftEval benchmarks that capture renn/eeasonallyy/neemnite patterns, typical of industrial forecasting applications. Our simulator, which we call SarSima (SARIMA Simulator for Zero-Shot Forecasting), is based off of a seasonal autoregressive integrated moving average (SARIMA) model as its core data source. Due to instability in the autoregressive component, naive SARIMA simulation often leads unusable paths. Instead, we follow three-step proce- dure: (1) we sample well-behaved trajectories from its characteristic polynomial stability region; (2) we introduce superposition scheme that combines multiple paths into rich multi- selltiisassn traces; and (3) we add rate-based heavy-tailed noise models to capture burstiness and intermittency alongside seasonalities and trends. SarSi i m0 is orders of magnitude faster than kernel-based generators, and it enables training on circa 1B unique purely simulated series, generated on the fly; after which well-established neural network backbones exhibit strong zero- shot generalization, surpassing strong statistical forecasters and recent foundation baselines, while operating under strict zero-shot protocol. Notably, on GiftEval we observe a "student- setttt-bbttt---cchhee effect: models trained on our simulations exceed the forecasting accuracy of the AUTOARIMA generating processes.
INTRODUCTION
Zero-shot learning fixes a pretrained model and predicts on target data with no parameter updates. While this paradigm has reshaped natural language processing and computer vision (Yosinski et al.) 2014|Wor et al. 2022), zero-shot time series forecasting is still in its infancy, but it is rapidly gaining
interest. Indeed, zero-shot forecasting (Garza & Mergenthaler-Canseer 2023 Gruver et al. 2023) offers compelling advantages for deployment scenarios, e,g. because using a frozen pre-trained model eliminates target-side selection loops and tuning heuristics. By collapsing rollout to pure inference no backpropagation, no per-dataset adaptation ceaptaatonn-zro----e zeoo-shot forecasting meets tight latency and cost envelopes, and it simplifies platform optimization (train once, reuse everywhere), while lowering compute and energy budgets per forecast. It also aligns with privacy and governance constraints: inference on sensitive targets remains strictly local, with no gradient flow or parameter updates that could leak information, easing compliance and audits. While recent work in time series forecasting focuses on architectural novelty (Liang et al. 2024). data is the lifeblood of zero-shot prediction. Curated compilations of real series can be helpful, but they inevitably run into problems, including licensing barriers, limited scale, and domain and cadence biases. Most problematic for zero-shot integrity is leakage: overlapping datasets in train/test, as well target-side hyperparameter search confound evaluation. Using just synthetic data has shown promise for zero-shot forecasting, but it has not yet been able to fully substitute for real data. For example, Ansari et al. (2024) show that augmenting real data with a kernel-basse synthetic generation procedure yields better results than using real data alone; however, they find training solely on synthetic data can significantly degrade performance; and Kuvshinova et al.] (2024) find that zero-shot pretraining on synthetic data is not comparable relative to using even small amount of real data.
In this paper, our goal is to bridge this gap and develop an effective synthetic-only training pipeline for zero-shot time series forecasting. Synthetic data offers unique levers: controllable coverage

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Published as a conference paper at ICLR 2026
of seasonalities and sampling rates, programmatic events, debiasing, and guaranteed leakage- free generation things that real compilations cannot easily match. Building on this premise, we provide the following contributions in this work. (1) We propose SarSimo, fast three-stage synthetic time series simulator (see Figure T that produces rich, realistic patterns and that is efficient enough synthesize sequences on-the-fly. fly, thereby enabling pretraining the scale of billions of series. To start, we first sample stable poles of the characteristic polynomial of a seasonal auto-regressive integrated moving average (SARIMA) process (Section 4.T. SARIMA provides natural choice as our simulator backbone both because it is deeply rooted in stochastic time series modeling, and because is fast and expressive, subsuming many other time series models as special cases (Hyndman et al. 2025). J. We also show that it captures the fidelity of real time series data with rich structure (Figure 3). Then, we introduce superposition scheme, combining sample paths for multi-seasonality via modulation (Section 4.2). Finally, we add rate-based heavy-tailed noise models to capture burstiness and intermittency (Section 4.3). (2)
We provide a detailed empirical evaluation of SarSim0 (Section (5) the M-Series (Makridakis al. [982] Makridakis & Hibon [2000]
Makridakis et al., 2020 |Athanssopoulos et 2011 and Gvf (Aksu et al.) 2024) benchmarks.
Our scope is zero-shot forecasting in industrial settings, where series are largely driven by complex trend, seasonality, and intermittency / heavy-tail patterns. M-Series and GiftEval, which span multiple domains (Nature, Web/CloudOps, Sales, Energy, Transport, Healthcare, Demographic, Finance, Industry, Macro/Micro Economic) and frequencies (yearly, quarterly, monthly, weekly. daily, hourly, and some sub-hourly). provide a comprehensive testbed for this regime. We find that training exclusively on time series generated by our simulator yields compact, fast, and accurate models that generalize under strict no-leakage guarantee. We show that, on these benchmarks, simulated data can be competitive with, or even outperform, real-data pretraining, substantially closing the gap between small efficient architectures and large foundation models; and on GiftEval, we see evidence for a "student beats teacher" generalization behavior. On the more regular, relatively short and low-noise business and macroeconomic M-Series, this effect mixed, with Aut OARIMA remaining very strong. This indicates that such emergent generalization is dataset- and domain- dependent, and is currently most pronounced on more heterogeneous and noisier benchmarks like GiftEval.
2 BACKGROUND
Univariate quantile forecasting. Let V1:t E R' be univariate time series observed up to time t. and let H be the forecast horizon. We aim predict, for each forecast horizon h 1...., H, a set of Q conditional quantiles of lt+h. We fix quantile levels = (7), TQ), 0 < < < TO < 1, and we define a lookback (context) window of length < T, x, == Ut-E+i= E RC, and forecasting producing quantile matrix, + Y (T)
model, Fo RR + R 2
T+1T+## with elements bfT)
Learning via Empirical Risk Minimization (ERM) with multi-horizon, multi-quantile loss. From a training corpus, we extract N supervised examples by rolling windows across one more univariate series, D = { (xx.,> Yt. 4t.+
We further define the quantile loss at level 7 as:
P+ (y. 0) (y- 0)+ + (1 (Ū y)+ with u4 := maxfu, O.. 0}. The multi-horizon, multi-quantile loss for single example i is:
H MΣ pr (vT+h, D12h))
CH.e(VT+IT-H, V
(I)
HQ
h=TTET
The ERM objective optimizing the network parameters v to approximate the conditional quantile function 7 + F=1 beth xx (T) on the grid T uniformly over horizons h I,..., I is then given by:
/ arg min
1
Σ LH, Fo(x)). (x.y)ED
NEW
N
Zero-shot forecasting. By zero-shot forecusting, we mean that we freeze all model parameters after pre-training a source corpus, and we then condition on a target series to make forecasts, while keeping the model parameters frozen. More precisely, following the definition of the zero- shot forecasting task from Oreshkin et al. (002)) and Olivares et al. (025)). let D(8) be a source training corpus and let D(?") be targer test corpus constructed from series disjoint from ((S) (no entity segment overlap). A forecasting model Fş is first trained on D(S) (all model selection
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is performed using splits of D(S) only), yielding parameters の². Zero-shot evaluation D(T) proceeds by applying the frozen (weights, normalizers, embeddings) predictor Fe-- to each target series independently, at time.
3 RELATED WORK
Transfer Learning. Early approaches to transfer learning in forecasting focused on frequency- specialized models (i.e., one model for monthly frequency, one model for quarterly frequency, etc). Success was measured by the model's s ability to outperform statistical baselines: AutOARIMA (Hynd) man & Khandakar| 2008), ETS (Holt) 1957). and Theta (Fiorucci et al. 2016), when applied to large time series corpora. Progress in this area has been driven by adopting cross-learning via training of global models on large time series collections to extract shared patterns; and this approach underpins the success of top- sop-pefforming models in competitions like M4 and M5 (Smyl] 2019 Anderer & Li 2022), as well as industry models such as DeepAR, MOCNN and TFT T (Salinas et al., 2020; Wen al. 2017 Lim et al. 2021). Zero-shot forecasting in time series emerged from transfer-learning formulations such as (Oreshkin et al. (002T) which showed that a frequency-spectn source-trained model can be deployed unseen series without target-side updates.
Foundation Models. Subsequent work moves beyond frequency-specific forecasters to- ward foundation-style pretraining, leveraging large sequence models for zero-shot prediction. TimeGPT (Garza & Mergenthaler-Canee Canseco 2023) pioneered the use of pre-trained transformers for forecasting, and LLMTime (Gruver et al. (023) extended this approach by adapting Llama (Touvron it al., 2023). Times adopts patch tokens and a decoder-only backbone for fast multi-step genera- tion (Das et al. 2024); ; MOTRAI RRI (Woo et al. 2024) couples patching with any-variate projections and mixture-likeliooe
heads for frose-freyuency robustness; and La g L.1 ama retains decoder-only design with lag features and parametric distribution heads (Rasul et al., 2024). Chronos adopts different approach by quantizing series values and uses encoder-decoder LMs with next-token cross-entropy for probabilistic decoding (Ansari et al. (024). Beyond attention, TTM targets accuracy- latency Pareto efficiency with alI-MLP mixers (Ekambaram et al. (2024). Recent work has highlighted subtle tradeoff's as training knobs are varied for different classes of models
(Yu et al.
2025b a)
Synthetic time series data. Forecast (Dooley al.) 2023) generates synthetic training
corpora by composing simple priors over trend and seasonal components, combined with multiplica- tive Weibull noise. KernelSynth from Chronos (Ansari et al. (024) augments real datasets with GP-kernel-basee synthetic samples. TimePFN (Taga et al. 2025) extends these approaches to multivariate settings using GP-kernel compositions and channel mixing. Unlike other approaches,
our simulator is grounded in stochastic time series dynamics (stable SARIMA) with broad expressive power (complemented with hierarchical seasonality and heavy-tailed noisers) rather than hand-crafted seasonal-tren templates or slow kernel synthesís. This yields high-fidelity temporal dependence, heteroscedasticity, and burstiness, while remaining orders of magnitude faster. Consequently, we pretrain foundation models exclusively on simulated data at scale; the resulting models exhibit strong zero-shot generalization across heterogeneous benchmarks, surpassing results of prior synthetic approaches (e.g., ForecastPEN. KernelSynthe
4 SARSIMO: TIME SERIES SIMULATOR PIPELINE
A central hypothesis of this work is that high-quality synthetic data can unlock scalable pretraining for zero-shot forecasting. In domains such as computer vision and natural language processing, foundation models are fueled by massive, diverse corpora. Time series, by contrast, suffer from (relatively) limited public datasets, licensing constraints, and pervasive risks of statistical leakage. realistic, efficient simulator offers an alternative path: it enables pretraining at scale while guaranteeing leakage-free evaluation. To this end, we propose a modular simulation pipeline, which we call SarSimO (SARIMA Simulator for Zero-Shot Forecasting). SarSim0 can be formalized as:
V1.T N o IoITo S(e).
Here S is a structured base-signal generator, Il is the interaction component that consumes tuples of structured signals and composes them into richer waveforms via parameterized interaction patterns (e.g., additive mixing multiplicative modulation); and N overlays the structured output with stochastic perturbations, including heavy-tailed noise to capture burstiness and intermittency. The overall Sa SarSim0 m0 system diagram, along with generated examples is shown in Figure The design
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seasonally
SARIMA
By
SARIMA-2
NOISERS
Generalzedd Gamma srape 0.5, rate 6, p-1.5
Log-normal shape 0.5. rate 6
Figure I: SarSimO simulator pipeline. Top: two base components are generated by SARIMA with AR (and scasonal) roots sampled via the characteristic polynomial inside the stability region, yiclding well-behaved paths seasonalities s =22 and s 7. Middle: SARIMA-2 superposition/modulaaiio block combines the components to produce a double-seasonal series with rich cross-frequency structure. Bottom: a noise module injects heavy-tailed disturbances: e.g., Poisson spikes, generalized-gane
bursts, and log-normal volatility capturing burstiness, intermitteney, and realistic deviations from Gaussian noise.
is guided by three requirements for effective pretraining: (i) structural fidelity to recurring motifs in real series (seasonality, trends, intermittency); (ii) scalability to billions of samples without storage overhead; and (iii) diversity sufficient to support generalization across heterogeneous benchmarks.
In this paper, for the base generator of SarSimo, we adopt SARIMA, because it combines deep statistical time series grounding with broad expressive power and computational efficiency. First, SARIMA subsumes many statistical models as special cases: it recovers Simple Exponential Smooth- ing. linear trend and seasonal Holt's 's method, well as damped-trent Holt- Winters variant (Hyndman al. 2025). Additionally, random walk (Naive), seasonal Naïve, Airline model (Box al. 2015).
and Theta method (Hyndman & Billah 2003a) formulations are all nested within the SARIMA
family, making a unifying lens for widely adopted forecasting approaches (Hyndman et al. 2025).
Second, SARIMA underlies the Aut cARIMA procedure (Hyndman & Khandakar 2008 which remains one of the strongest zero-shot baselines in forecasting competitions and applied practice. By grounding SarSim0 in SARIMA, we inherit the statistical foundations of classical models and retain a direct link to Aut OARIMA as a natural "teacher", while aligning with and complementing the inductive biases of neural "student" architectures. We will that outperform AutOARIMA; moreover, as Figure Jshows, SARIMA reproduces the statistical structure of real-world time series, providing credible training signal.
models
4.1 SARIMA SIMULATOR
Without loss of generality, we start the exposition with the Auto-Regressive Moving Average (ARMA) process of order p', that can be defined as:
y/ - 01
Onllt- = Et + 018,-1 + dyet-q-
Here 01:pp' auto-regressive coefficients, di.g moving average coefficients, and Ez-gst zero-mean i.i.d. innovations. With the lag operator L defined as Lyf: = Yr-1, this process can be written compactly in polynomial form:
(1
P
1
L (1 (1- 1)"
1
(4)
i=1
where p p' d and coefficients ó are derived from coefficients a factor out d unit roots of the polynomial, corresponding to the finite difference time domain integrator, 3/ +- Ye + 3t-1- Consequently, ARMA with integrator (d 0) is called ARIMA (integrated ARMA).
In principle, ARIMA could be used directly as a time series simulator, by randomly generating initial state you orders p' q; coefficients a, it; excitation noise E, and unrolling Equation ( through time. However, as shown in Figure 2 (bottom), setting the coefficients arbitrarily destabilizes the system and results in divergent nonsensical time series that are not useful for training forecasting
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AR poles
Simulated Time-series
-10
2
10
20
60
AR poles
1e22
Simulated Time-series
0.5
0.0
-0.5
-2
10 20
30 40 50 60
Figure 2: Sampling of SARIMA poles by SarSim0. The SARIMA order-10 AR process poles are shown along with the unit circle the left. The resulting generated processes with these poles are shown on the right. The top pane shows poles sampled according the proposed procedure, resulting in realistic looking time series. The bottom pane shows the result unconstrained random generation of AR coefficients. resulting in divergent time series that is useless from the perspective of training time series foundation models.
model. To circumvent this stability issue, we propose instead to operate directly in the model's pole space, guaranteeing valid process dynamics by construction. In particular, there is a link between the summation-baas polynomial form 44) and the product-based pole representation:
(LL) = Σ
P. II p.
(5)
bell-bbchveednes of the AR part is guaranteed if the poles, Pis lie within unit circle, |po| (Hamilton) 1994] Chapter 3). Thus, we propose sample the poles of the AR and MA transfer functions, [p:)] and (0) 1 respectively, and then derive the system coefficients a and from the pole representation using product expansion (e.g.. numpy's np.poly). A typical realization of the process sampled using this approach is shown in Figure 2 (top). In contrast to Figure (bottom), all poles of the AR system are located within unit circle, resulting in a well-behaved simulation result.
<
To complete the polynomial specification of the base SARIMA, we include the seasonal part with parameters (period), D (integration order), P (seasonal AR order), Q (seasonal MA order):
P
L
1, j=1
(1- (1- 1.) (1-))
1
Σ ==1
O,L
E7.
3=1
We note that the AR side is the joint lacunary (sparse) polynomial A(L) = 1 Ei OLL' Σ/= 2, (L In the additive form, joint stability is non- factoriziii:::: A does not split into inde- pendent nonseasonal and seasonal factors. This nonseparability. together with the gappy support {I.....p) U {s, 2s..... Ps}. makes the stability region nonconvex and numerically thin: small changes in (1), 4) can move poles across the unit circle, especially near seasonal frequencies. There- fore, to obtain well-behaved simulations, we adopt a mixture approach: with probability 0.5 we draw an AR-only model (0) for all j) and with probability 0.5 a seasonal-AR--o AR-only model (dy 0 for all i); each subcase is trivial to stabilize.
These considerations lead to the following practical algorithm for sampling a general SARIMA process. First, sample model orders p. 9, P. Q uniformly at random (from 0 to the maximum integer value defined for each of them). For the AR side, flip fair coin and set either = or P = 0 with probability 0.5. Then, once the model order is defined, sample poles uniformly within the unit circle by first sampling the radius uniformly between and Tmax and then the complex angle [o, 2x). Next, convert roots to coefficients by expanding the poles product into polynomial form (e.g., Equation 5): we also set the integration order to tend to be numerically unstable. Finally, sample the warmup trajectory state V1:w and innovations process Ei: from i.i.d. zero-mean normal distribution, setting w = max(p, q. P.s. Q.s, d+ D.s), and unroll the SARIMA process according the following time-domain recursion starting
and D = 1, since higher integration orders
w 1:
q
Vt
bilt- i
Σ L 1 j-a
0,5 f=1
Σ
θ Ofet-j- t
(6)
1=1
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We apply the non-seasonal and seasonal integrators a separate pass (ye f Yt + 3t-1+ Yr Yt + 3/t=)). To produce more diverse trend patterns, we further enrich the integration framework by subjecting y/ to a fractional differencing operator, which results in simulating fractional integration orders between O and (by sampling fractional difference order d' uniformly at random in [0, 1)). We approximate the fractional differencing operator by a finite impulse response filter with binomial coefficients, following the work of Hosking (1981] 2; = l' - d') (i + 1)). Simulating trajectories via the recursion O6) is reasonably fast, but the time dependence imposes a sequential loop that cannot be vectorized across time. To remove this bottleneck, we vectorize across trajectories: for each sampled parameter tuple p. q. P. Q, s, d', we draw B independent sets of initial conditions (and innovations), and we unroll B paths in parallel. This delivers substantial speedups from vectorized computation and preserves diversity as distinct initial states yield diverse realizations under the same parameters.
4.2 SARIMA-2 SIMULATOR
Many real-world series exhibit bi-seasonality; fast rhythm modulated by slower envelope. Examples include road traffic, web activity, call-center volumes (intra-day peaks modulated by weekday effects) -Moreira-Matias al., 2013 [Strowes] 2016; Ibrahim & L'Eeuyer| (016); electric load (intraday cycles shaped by weekday and annual patterns) (Hong & Fan 2016). Single-sesson models capture the fast cadence but miss amplitude modulation and the induced heteroscedasticity. These observations motivate a compositional construction with two seasonal processes: one high- frequency "base," and one low-frequency "envelope." " whose additive or multplicatiiv interaction reproduces the envelope-on-carte introduce SARIMA-2, which composes two independent, pole-stable SARIMA processes: high- frequency base series y y and freeurruency envelope series y(+), The envelope is upsampled to the base rate and combined with the base either additively or multiplicatively:
structure observed in practice. To model this structure, we
Additive:
1/
y1 + yi
(b)
(e)
Multiplicative: Ut - (1 + w Di V1 (8)
(8)
where, in the multiplicative case, y/ is normalized to [-1, and modulation depth, w. is sampled from Uniform 1). This composition induces controlled amplitude modulation, capturing effects such as weekday intensity swings. We show an input-output pair for multiplicative SARIMA-2 in Figure (middle).
4.3 NOISERS
Many domains exhibit statistical features that cannot be captured by seasonal dynamics (that have a given time scale) alone. Retail and spare-part demand often shows intermittent spikes and long runs of zeros, motivating Poisson- or count-based models (Croston] 1972, Syntetos & Boylan 2005). Internet traffic and web workloads are well known to follow heavy-tailed distributions and exhibit burstiness across multiple time scales (Willinger et al.) 1995 Feldmann et al. 1998).
Environmental processes such as daily precipitation amounts are classically modeled with Gamma- family distributions, highlighting the need for positive, heavy-tailed shocks (Wilks) 1999: Ghil et al. 2002). Together, these examples establish that real-world series frequently combine heterosceaasticity, intermittency, and heavy-tailed disturbances with their seasonal structure. To capture these effects, our simulator incorporates a dedicated Noiser module, N, which implements the random rate noise process:
T] (A). d = g(yc) 2 O,
where Ye is the structured signal (output of SARIMA or SARIMA-2), g(-) maps level to time- varying rate (c.g., normalization plus a log-uniform scale), and x denotes the distribution's 's shape hyperparameter(s). The rate X, ties variability to the local mean level (heteroseedasticctty), while governs the distributional form, typically controlling overdispersion and skew (e.g., for the Gamma distribution the coefficient of variation is 1/V (Johnson et al. 1994)). Thus, X sets the scale of fluctuations conditional on yt, and x calibrates how those fluctuations are distributed (spread, asym- metry, and tail behavior). We implement three complementary noiser families: Poisson, Generalized Gamma and Lognormal. All noisers condition their variance on the local series level. normalized by series min and max values and scaled by the rate intensity sampled from LogUniform:
X Ao(Ue min y:)/ (max Dr- -mjn y)): do ~ LogUnioornon/aaan Amax]-
(9)

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Figure SarSim0 Fidelity with Real time series Data. Center: UMAP embedding space 60-step windows from real dataset M4-Monthly (red) overlaid on equal-length samples from SARIMA simulator with uniformly sampled seasonality E (O.... 24) (blue). Left and right: real (red) and synthetic (blue) series drawn from the circled regions. Key take-aways include: (1) the simulator spans the scasonal regimes real data (e.g., M4-M M4-Monthly). including the overall dataset as special case; and (2) within scasonality, synthetic series closely match real exemplars co-located the embedding space, yiclding realistic, fine- mne-grained patterns.
Poisson noiser generates level-dependent count spikes characteristic of intermittent demand and arrivals, ~ (ooss Generalized Gamma noiser introduces controllable burstiness by sampling from gamma distribution, 1/1 Gamma Xt R),,
LogUniform [Kminn kimaax] and further applying a random power transform 1) = [/ Ç Uniform Smax]- Lognormal noiser produces multiplicative, heavy-tailed shocks that emulate volatility fluctuations by sampling T/2 ~ LogNormal (Ae, k), к LogUniform [Kmin Kmax] This combination provides a compact, simulator-friee friendly toolkit to reproduce the main classes of non-Gaussian level-dependent distur- bances observed in practice, while remaining efficient for large-scale, on-the-fly generation. The
examples of noise traces produced by the three Noisers are provided Figure [ (bottom).
EMPIRICAL RESULTS
In this section, we evaluate SarSim0 along five axes. (i) Fidelity: Do synthetic series reproduce the statistical structure of real data, providing credible training signal? (ii) Generalization: Does pretraining simulated data yield models that transfer zero-shot to heterogencous real datasets, and how does performance compare models pretrained on real data (e.g,, Chronos, Moirai, T mes)) (iii) Architecture robustness: Can architectures with distinct inductive biases, trained on synthetic diversity at scale, reach performance competitive with recent neural forccasters; and can dcsene substitute for architectural complexity? (iv) Sludent-beats-ters models trained only on simulated data outperform their "teacher" (i.e., Aut OAR derived from SARIMA) real benchmarks? (v) Ablations: Do each of the proposed components. SARIMA, SARIMA-2, and the Noisers, contribute measurably to zero-shot generalization? We start by detailing benchmarks, baselines, training and testing protocols, followed by quantitative results and ablation studies addressing these questions.
effeect: Do
5.1 BENCHMARKS
GiftEval is curated benchmark for evaluating time series foundation models: models are applied to standardized test splits from 23 datasets spanning seven domains and ten sampling fiequencies. The benchmark reports results for an array of statistical, deep, and foundation baselines (Aksu et al. 2024).
The detailed composition of the benchmark and constituent datasets is provided in Appendix A
M-Series is composed of four forecasting tasks comprising over 100,000 time series, curated from established forecasting competitions: M1 (Makridakis et al. 1982), M3 (Makridakis & Hibon 2000), M4 (Makridakis et al. 2200)), and Tourian (Athanasopoulos et al., 2011)) These datasets, summarized in Table Appendix represent broad range of domains and temporal frequencies.
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GiftEval
M-SERIES
Inference Time (m)
sCRPS
MASE
sCRPS
MASE
Zero-Shor Shot
Chronos-Base
0.647
0.870
0.103
0.878
2103
Chronos-Small
0.662
0.892
0.103
0,882
702
MOIRAI-Large
0.599
0.874
0.128
1.027
3976
MOIRAI-SmalI
0.650
0.946
0.124
1.089
994
ITM-RR-Pretraieed
0.873
1.020
0.155
1.118
43
TimesFM
0.680
1.077
0.098
0.930
155
NBEATS
0.815
0.937
0.095
1.134
271*
X
PatchTST
0.587
0.848
0.090
1.613
165*
X
AutoARIMA
0.912
1.074
0.096
0.843
420
X
NBEAT9-Kerneil@nthh
0.686
0.978
0.116
1.033
NBEATS-ForecasttEN
1.070
1.354
0.113
0.979
PatchTSS-KerreelSyythh
0.702
0.977
0.119
1.051
PatchTsT-FPreeasttPP
1.060
1.346
0.105
0.949
Chronos-Kerneel@ynnhh
0.688
0.987
0.113
1.003
Chronos#ForecastPPN
1.283
1,575
0.118
1.001
NBFATS-SarSim0
0.602
0.849
0.096
0.869
46
PatchTST-SarSinm
0.573
0.837
0.097
0.877
47
Chronos-SarSiml
0.608
0.878
0.100
0.896
52
MLP-SarSimO
0.643
0.907
0.109
0.982
45
Table 1: Performance on benchmarks, weighted aggregation over datasets. Lower values are better. In the second block. AutoARIMA is fitted on each test series, while NBEATS and FaT T are trained from scratch the training split of each dataset (inference time with includes training time). A green checkmark denotes models evaluated under a strict zero-shot protocol, a yellow checkmark denotes pretrain-test overlap (details in Appendix([] ( and a red cross denotes non non-zcro-shor zcro-shot baselines. Key take-aways include: (1) SarS SarSim0 i.0 enables strong zero-shot forecasting from synthetic data alone, even outperforming real data pre- pre-training; (2) Sars imm outperforms alternative NBEATS with SarSim0 close the gap and even slightly exceed large models like Chronos; architectures pre-trained on SarSim0 outperform AutoARIN derived from SARIMA generating process.
expensive synthctic data pipelines, such as Kernel 1ynnch (3) small models such
GiflEval,
To ensure the comparability of work with the existing literature, evaluate the accuracy of the forecasts using well-established metrics: scaled Continuous Ranked Probability Score (sCRPS, (Gneiting& & Raftery] 2007)) and Mean Absolute Scaled Error (MASE, (Hyndman & Koehler 2006)). defined in Appendix D M-Series results report average sCRPS and MASE across datasets weighted by dataset size. Gillval results report geometrie mean of sCRPS and MASE of each method
divided by sCRPS and MASE of seasonal naive each dataset (Aksu et al., 2024). Importantly, in both benchmarks, we use the datasets solely for evaluation purposes excluding them from model optimization-to assess the zero-shot forecasting capabilities of our models.
5.2 BASELINES TRAINING METHODOLOGY
We consider a collection of well-established baselines that includes AutoARIMA from
StatsForecast. (Garza et al. 2022). Neural forecasting baselines trained on the train splits of target datasets are represented by NBEATS (Oreshkin et al.) 2020) and PatchTST (Nie et al. 2023)
In terms of foundation models, we use publicly available pretrained checkpoints of Chronos (Ansrii
al. 2024). TimesFM (Das al. 2024), MO MOIRAI (Woo al. 2024), and TTM (Ekambaram et al. 2024.. Our proposed simulator is trained on NBEATS, MLP (a single block of NBEATS), PatchTST
and Prronos-Small T5. These models represent very different types of inductive biases (fully- connected design vs. attention- based and patching designs) and all are generally accepted as strong baselines in the literature. Models are implemented in PyTorch (Paszke et al.) 2019) and trained for 250k (NBEATS) and 500k (PatchTST, Chronos) steps. Models predict $12 horizons ahead in one shot. Further details and hyperparameter settings along with SarSim0 simulator settings appear in Appendix E In all cases, trained models applied at inference time with no tuning of parameters or hyperparameters on test datasets. In addition, NBEATS, PatchTST and Chronos trained two baseline synthetic data generators, ForecastPFN (Dooley et al. 2023) and KernelSynth (Ansari et al. 2024) to assess Carsimo' 's effectiveness w.r.t. existing methods. Forecast PFN training the exact same settings as Sarsi im0, whereas for hernelSyne
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Table D also lets us probe question: can models trained solely synthetic trajectories de- rived from SARIMA exceed their statistical "teacher" (AutOARIMA derived from SARIMA) on real data? On GiftEval, NBEATS- SarrS-SaSSa. Sim,, PatchTsT-SarSime and Saronos-SarSiin achieve markedly lower sCRPS and MASE than Aut CARIMA. On the M-series benchmark, the matches sCRPS, but it is slightly worse in Published as a conference paper at ICLR 2026
GiftEval
M-SERIES
sCRPS
MASE
sCRPS
MASE
PaLcchSST-Sarsino-SOOK
0.573
0.837
0.097
0.877
PatchisT-SarrSin--22
0.576
0.838
0.102
0,922
No SARIMA-2-250K
0.647
0.926
0.103
0.929
No Noisers-250K
0.594
0.859
0.096
0.861
NBEATS-SarSimo
0.602
0.849
0.096
0.869
No SARIMA-2
0.655
0.913
0.104
0.941
No Noisers
0.609
0.856
0.096
0.860
Table 2: SarSimo ablation, where lower values are better. Key take-aways include: (1) Removing SARIMA- 2 causes the largest accuracy drop across backbones and benchmarks, positioning it important generalization driver. (2) Removing Noisers has dataset- and model-dependent effects. For PatchTST and limited train budget of 250K iterations, this hurts on GiftEval, but it helps on the more regular M M--rriis. For extended training budget of 500K iterations, PStchTST with Noisers recovers performance on the M-Series, while retaining stronger results on GiftEvvl.
were only able generate and save to disk up to 10M time series (which is 10 times the scale of synthetic data reported in (Ansari et al.) 2024)) of length 1024 due to the very slow generation process (see Figure in Appendix F for speed comparison of synthetic pipelines).
5.3 RESULTS
We begin by exploring the fidelity of the proposed SARIMA-basee simulator in relation to real time series data. As an illustration, Figure3shows a joint UMAP of z-scored 48k windows (60 steps) from M4-Monthly, containing monthly time series rich with (a) trends and (b) monthly scasonalities with period 12 from demographic, finance, industry domains (Makridakis et al. 2020). and 384k equal- length SARIMA samples. Two features are particularly apparent. (i) Seasonal strata: Uniformly sampling the seasonal period E (O.....244 yields blue clusters that align with 8; some align with the red M4 modes, indicating that SARIMA'S seasonal knob reproduces and extends the dominant structure of the real data. (ii) Local co-location: Within each stratum, real and synthetic windows intermingled; because UMAP preserves local neighborhoods, intermingling suggests match in short-lag autocovariances and narrowband peaks, not just marginals. Together with the side-panel look-alikes (instance-level fidelity), these observations make SARIMA plausible data engine for pretraining forecasters capturing relevant seasonal modes, and reproducing local dynamics.
Our key results on generalization and architecture robustness appear in Table showing aggregate metrics across two benchmarks. Models pretrained solely on our synthetic data achieve strong zero-shot generalization across heterogeneous benchmarks. In particular, NeEATS-SarS imo, and Chronos SarSim0 consistently outperform their counterparts trained on prior synthetic approaches (Kernel (KernelSynth, Synth, ForecastPFN), and they even more than close the gap large real-data- dada--pettranne models (i.e., Chronos, MOIRAI, Time FFM TTM-R2). The results support the claim that our simulator provides a sufficiently rich training signal to transfer across domains without exposure target data. Moreover, the relative gains of NBEATS-SarS? m0,, Pat.chTTT-Sar Simo m0 and Chronos -SarS 1im0 highlight architecture robustness: architectures with distinct inductive biases reach competitive performance when trained on the same synthetic corpus. Together, these results suggest that diversity and scale of simulated series can partially com- plement and substitute for architectural complexity. Beyond aggregate scores, stratify GiftEval results by domain, sampling frequency, term length, and variate type (Appendix H.3). Across all splits, SarSine iiriimmmm preerrpid backbones are consistently competitive with, and often stronger than, real-data foundation models. At the same time, SarSimo uniformly outperforms prior synthetic generators (KernelSynth, ForecastPFN) and often matches or surpasses strong per-dataset super- vised NBEATS/P& chIST baselines. This indicates that a single, domain-agnostic SARIMA-basel curriculum transfers robustly across GiftEval's ' diverse regimes.
PatchTST-Saree
evidence is mixed. For example,

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Published as a conference paper at ICLR 2026
MASE. Overall, despite being trained on SARIMA- -eeeerr-eeeeeteed data, these neural forecasters exhibit predictive capacity that extends beyond their generative teacher. While Table [ is based on the full SarSim0 (including SARIMA-2 and Noisers), which is not exactly expressible single AutoARTMA specification, Table 22 in Appendix H..4 shows that NEEATS trained only on pure SARIMA samples leads to the same qualitative conclusion.
Finally, we tackle the Ablation axes. Looking at Table 2 we conclude that removing SARIMA-2 (the interaction layer) causes the largest drop in zero-shot accuracy for both PaT and NBEATS, uniformly across benchmarks, suggesting it as a strong driver of generalization. Removing the Noisers has clear model- and brrchmaark-deendemn effects. For PatchTST, for instance, we find that more iterations (500K vs. 250K) are needed to fully benefit from Noisers. This points to a practical trade-off: under tight compute budgets, a simpler simulator configuration and backbone may be preferable, whereas with more generous budgets, the full SarSim0 pipeline and more expressive backbones yield, in our experiments, stronger overall zero-shot performance. In addition, we performed the BarSimo hyperparameter sensitivity study (see Table 13 in Appendix details). Across studied configurations, performance on both GiftEval and the M-Series remains very similar to the default configuration, indicating that SarSim0 is not at brittle "sweet spot" in design space. The configuration we use (details in Appendix E.3 appears to be munchmark-agnoste and robust substantial hyperparameter changes.
H.2 for
To probe behavior far outside our target regime of business-style series, we also ran a zero-shot experiment four canonical nonlinear dynamical systems (Duffing, Lorenz, Lotka-Volterra dulum), comparing several Chronos variants, T TimesFM, and SarSim0-pretraing Volterra, Pen- Appendix H.I for details). SarSimO-pretraing data foundation models. This suggests that SarSim0 's inductive biases, while geared toward trend/ hta////saoonniiiittttttgggg regimes typical of industrial forecasting, yield models whose out-of- domain generalization is similar to that of real-data- data--ppetttaanedde models on these systems.
models (see models attain error levels comparable real-
6 DISCUSSION
By introducing SarSim0, we have shown that it is possible to achieve competitive zero-shot forecast- ing through training on simulated time series data alone. By enforcing stability in autoregressive pole sampling. introducing hierarchical scasonality through superposition, and overlaying heavy-tailed noise processes, our SarSimo simulator generates trajectories that are fast to generate, privacy- and license-safe, and sufficiently realistic to train models that generalize across real datasets. Central findings. First, on GiftEval and the M-Series, simulator-only pretraining achieves competitive zero- shot performance and sometimes exceeds real-data pretraining, suggesting that simulator fidelity, scale, and diversity can matter as much as architectural inductive biases. Second, we also see that our synthetic data pipeline can more than close the gap between small architectures and large pre-trained models such as Chronos, again highlighting the power of data generation. Additionally, Gil we observe early, benchmark sppecffcc evidence of a "student- seadeeett-bbttteaccttte teauhhrt effect. Global neural models pretrained on SarSimi whose core stochastic assumptions mirror the SARIMA family underlying Aut AAtIIAIMM, can outperform this strong per-series Aut outoOAII IMA baseline. This suggests an emergent form of generalization beyond the simulator components, motivating further exploration of synthetic-first training for time series foundation models. Limitations. There are many exciting presents novelty analysis comparing the SARIMA distributions against M4-monthly using Local Outlier Factor detector. A consistent and interpretable pattern emerges among the most novel real windows: they typically exhibit (i) abrupt level shifts or structural breaks (e.g., changes in trend slope or regime changes in the underlying process), and (ii) strong, isolated spikes or outages that do not repeat seasonally (especially iso- lated aperiodic negative spikes). This motivates natural extensions of SarSimo based on richer volatility and regime-switching structures (e.g., GARCH-style components or regime-switching SARIMA), which we leave important future work. While expect hybrid synthetic-real training to outperform either source alone in many practical settings, we deliberately focus on the clean synthetic-only zero-shot regime, leaving synthetic-real co-training work. Exogenous covariates are also not considered. Finally, it would be particularly fascinating to understand in detail when and why learners can surpass their generative teachers.
directions for future work. For example, Appendix G
important direction for future
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Haoyi Zhou, Shanghang Zhang. Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang. Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting. The Association for the Advancement of Artificial Intelligence Conference 2021 (AAAI 2021).,
2020. BRthhtts:///ae httt::ps//arra...or//aa///////// 07436
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A GIFTEVAL BENCHMARK
Table 3: Summary of GvftEval forecasting datasets used in our empirical study,
Frequency
Series
Jena Weather
Autoloemer (Wo et 202()
Nauare
101
52,701
52,701
52,701
$2,704
Jeno Weather
Autoformer (Wu al. 2021)
Navare
11
8.784
8,784
8,784
8,784
Jena Weather
Autoloemer (Wu et 2021)
Nature
D
356
365
305
366
BotTTes Application
AutoMiser (Pilasker et al. 2024)
WalChadOpp
RGS
1
8,834
8,834
8,844
8,534
BialTOts Service
AutoMixer (Palaskar et al. 2024)
WebsChndOpe
10S
21
8,835
8.835
8.835
185,535
BiviTObs-1
AutoMiser
2024)
WaleClndOpp
31,068
31,968
Bis L2C
AutoMiierr (Palaskar
WeaCCouOOps
2,064
2,064
Rithenins Storage
Workloass Archive (Slicn
WewChoddOpa
1,250
8,640
8.640
8.640
10,000000
Bicbrains Fast Storage
Grid Worklodds Archive (Sben 2015)
WesCCondOpe
11
1,250
72]
721
721
901.250
Bitheins-- md
Grid Workloods Archive (Shun al 2015)
WewClondOpp
ST
500
8,640
8,640
8,540
4.3 4,3200000
Bobrains md
Grid Workloods Archive (Sben et 2015)
WesClondOps
11
500
720
720
720
3600000
Restaurant
Recnuit Rest. Comp. (Howaod et 2017)
Sales
D
R07
358
G7
478
289.203 203
ETTI
Informer (Zhou al. 2020)
Energy
15T
68,
69,680
69.680
Infoemer
Energy
17,470
2020)
Energy
725
125
Infoome: (2hon al. 2020))
Enesgy
105
103
Informer (Zhou et al. 2020)
Energy
1ST
69, 680
69,69 680
680
69,680
ETT2
Intormer (2hou et al. 2020))
Energy
H
17,420
17,420
17,420
17,420
ETT2
Informer (Zhou et 2020)
Energy
D
725
725
725
725
ETT2
Informes (Zhon et 2020))
Energy
W-THU
103
103
103
Loep Seattle
LabCiy (Wang 20233a
Transpett
ST
323
105, 120
105, 125
105, 150
33.953,760
Loop Scuttle
LibCay (Wang 2023al
Transport
1
323
8,760
8,760
8,760
2.8294800
Loep
(Wang 2023al
Transport
365
LabCry (Wang 202361
Transpoct
15T
156
2,776
1,976
19776
264.256
LabCyy (Wang 2013a)
Transpett
H
156
744
244
116.64
M_DENSE
LibCly (Wang
2023al
Transpoct
H
17,520
17,520
17,520
$25.000
M. DENSE
LaCry (Wang et 2023a)
Transport
D
30
730
730
730
21,500
Solar
LSTNGr (Lai et 20177)
Energy
10T
157
$2,560
$2,560
$2,560
7.20X.220
Solar
1.TNN (Tai et 2017)
Energy
H
157
8,760
8,760
8,700
1,200.770
Solar
LSTNet (Lai al. 2015)
Energy
D
137
365
365
50005
LSTNet (2020)
Energy
W-TRI
Hicrasciical Sales
118
1,825
L,25
215,350
Hicrachical Soles
Manento (2020)
Sales
118
260
260
30,600
Yearly
Monach (Godabewa et 2021)
Eccn/Fin
A-DEC
22,974
37
19
284
865.109
M4 Quarterly
Monuch (Godahewa al. 2021)
Eccn-Fin
Q-DEC
24,000
100
24
874
2,406, 108
514 Monthly
Monnsh (Godihewa.c al. 2021)
Eccn/Pin
M
48,000
254
60
2.112
11,266411
M14 Warkly
Monach (Godihows al. 2021)
FacefFin
W-SUN
359
1,035
93
7,610
371,579
Daily
Monadh (Godihewa al. 2021)
EcondFin
4,227
2,571
9,933
10,023,866
Hourly
Monadh (Godillewa 20121)
Eccn/Fin
414
375,372
Hospocal
Monash (Godshewa 2021)
Healthcure
767
64.428
Monsah (Godshowa
2021)
Haaltheaae
266
212
$6,992
US Births
Monach (Godsbewa 2021)
Heallheare
D
7,305
7,305
7,305
7.305
US Births
Monadh (Liddahewa al. 2021)
Healtheare
WITUE
1,045
LJ145
1,043
1,43
US Births
Monach (Godahewa al. 2021)
Healtheure
M
240
240
240
240
Sangeen
Monnch (Godihewa al. 2021)
Nitare
D
23,741
23,741
23,741
23.74
Suggeen
Monadh (Godshewa 2021)
Nature
W-TITU
3,391
3,391
3,391
3,391
Sangeen
Monadh (Godiheewa
Nature
780
Temperature
(Godshewa 2021)
Nature
32,072
725
Cup
Monnah (Godshiewa
2021)
Notwe
H 270
10,898
9,504
10,920
2.942.964
XDD Cup 2018
Monach (Godhhea
2021)
Nacure
D 270
396
455
122,791
Car Purts
Monadh (Goddihewa et 2021)
Sales
M 2,674
51
51
51
136.374
Electricty
UC] ML Arclive (Trindude 2015)
Energy
15T
370
140,256
140.256
140,256
51,8947200
Elaenicity
UCI ML Archive (Trindade 20155)
Energy
H
370
35,064
35,064
35,0644
12,973,600
Electricity Electniity
UCI ML Anchive (Trindule 2015)
Energy
D
370
1,46]
1,461
1,461
$40.570
ML Archive (Irindade
W-FRI
208
76,960
In this section, we discuss details of the evaluation GiftEval datasets. The benchmark incorporates data from ten sources, beginning with the Jena Weather dataset, from the Autoformer (Wu al., 2021). Business and IT observability data from BizITObs (processed via AutoMixer's pipcline) includes Application, Service, and L2C metries that combine business KPIs with IT event data (Palaskar al. 2024). This is complemented by cloud workload data from Bitbrains via the Grid Workloads Archiv (Howard et al., 2017). For energy-related applications, we incorporate electricity transformer temperature datasets (ETTI and ETT2) from Informer (Zhou et al. 2020), crucial for long- power deployment monitoring; and urban transportation time series come from LibCity (Wang et al.,
2023 Solar plant energy output predictions are sourced from LSTNet (Lai al. 2018), and sales forecasting data are from Mancuso et al. (2021). We also include carefully curated subset of the Monash time series collection, selected to avoid overlap with pretraining data (Godahewa
2021), and electricity consumption patterns of 370 clients from the UCI MI. Archive (Trindade
2015). provides detailed statisties for each dataset, including source information, frequency, prediction length, number of variates, series length, and total observations.
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B M-SERIES BENCHMARK
Table Summary M-series forecasting datasets used our empirical study.
Frequency
Seasonality
Horizon
Series
Min Length
Max Length
% Erratic
Monthly
12
18
617
48
150
0
M1
Quarterly
4
203
18
114
0
Yearly
181
15
Other
4
174
71
104
0
Monthly
1428
66
144
2
M3
Quarterly
4
756
24
72
1
Yearly
645
20
47
10
Hourly
24
48
414
748
1008
17
Daily
1
14
4,227
107
9933
2
Weekly
359
93
2610
M4
Monthly
48,000
60
2812
Quarterly
4
24,000
24
874
11
Yearly
23,000
19
841
18
Monthly
12
24
366
91
333
51
Tourism
Quarterly
4
427
30
130
39
Yearly
518
11
47
23
In this section, we discuss details of the M-series data.
B.I MI DATASET DETAILS
The M1 competition (Makridakis time series of varying frequencies and lengths (9-132 observations). The competition revealed that simple methods like ETS (Holt 1957) often outperformed complex ones, establishing a legacy emphasizing accuracy, automation, and parsimony in forecasting practice.
1982) analyzed 1,001 demographic, industrial, and economic
B.2 M3 DATASET DETAILS
The M3 competition Makridaaiss & Hibon 2000), held 20 years after M1, analyzed 3,003 time series from various domains, with 14-126 observations and multiple frequencies. The competition reaffirmed the superiority of simple forecasting methods, with the Theta method (Hyndman & Billah 2003b) emerging as the top performer.
B.3 M4 DATASET DETAILS
The M4 competition marked substantial increase in both size and diversity, comprising 100,000 time series across six frequencies and multiple domains. The competition introduced prediction interval evaluation and featured 18 percent smoohh series (Syntetos al., (005). Notably, neural network model (SRRN(Smyl 2019). outperformed traditional methods for the first time, helping popularize cross-learning (Semenoglou al. 2021) global models.
B.4 TOURISM DATASET DETAILS
The Tourism dataset (Athanasopoulos al. 2011
designed evaluate forecasting methods
applied to tourism demand data across multiple temporal frequencies. It comprises 1,311 time series monthly, quarterly, and yearly frequencies. This competition introduced the Mean Absolute Scaled Error (MASE) as alternative metric to evaluate scaled point forecasts, alongside the evaluation of forecast intervals. Notably, 36% of the series were classified as erratic intermittent. Due this high proportion of irregular data, the Naivel method proved particularly difficult to outperform the yearly frequency.
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C DEVIATIONS FROM THE GERO-SHOT SETTING IN BASELINES
Table Summary of zero-shot deviations from baselines. Checkmark indicates that a given dataset used to pretrain given model.
Dataset
Source
Chronos
TTK-R2
MOIRAI
TimesEk
Monash (Godahewa 2021)
X
M3
Monash (Godahewa 2021)
Monash (Godahewa 2021)
X
Tourism
Monash (Godahewa 2021)
X
Jena Weather
Autoformer (Wu al. 2021)
BizITObs
AutoMixer (Palaskar al. 2024)
X
Bithrains
Grid Workloads Archive (Shen et al. 2015)
X
Restaurant
Recruit Rest. Comp. (Howard et al. 201
X
ETT
Informer (Zhou et al. 2020)
X
Loop Seattle
LibCity (Wang et al. 2023a)
S7-Taxi
LibCity (Wang et al. 2023a)
M_Dense
LibCiit (Wang et al. 2023a)
X
X
Solar
LSTNet (Lai ct al. 2017)
Iierarchical Sales
Mancuso et al. (2020)
Hospital
Monash (Godahewa
2021)
X
COVID Deaths
Monash (Godahewa al. 2021)
Births
Monash (Godahewa 2021)
Saugeen
Monash (Godahewa 2021)
Temperature Rain
Monash (Godahewa 2021)
KDD Cup 2018
Monash (Godahewa 2021)
Car Parts Electricity
Monash (Godahewa 2021)
UCI ML Archive (Trindade 2015)
In this section, examine in detail how the baselines reported in Table I deviate from strict zero- shot forecasting regime, as defined in Section g While several recent models have been described as "foundation forecasting models" many rely directly on the evaluation datasets training data. As result, their performance can not be interpreted as that of a foundation forecasting model.
Chronos (nsari al., 2024) paper explicitly distinguishes between pre-train only, in- domain, and zero-shot evaluation settings. Unfortunatedly, several of the datasets they include in their in-domain evaluation regime (Table of their paper) overlap with the GiftEval and the M-series benchmark collections. The datasets include M4, Solar, KDD cup and Electricity.
TTM-R2 (Ekambaram et al. 2024) model was introduced in the context of long-horizon forecasting, and not framed as zero-shot model. More recently, TTM-R2 and its fine- tuned variants have been explicitly adapted to GiftEval through task-specific fine-tuning, which further departs from the zero-shot foundation model definition ! The deviations from the zero-shot regime include the Long-horizon Weather dataset, Loop Seattle, Taxi, Solar, Hierarchical Sales, and a big subset the Monash repository in Hospital, COVID deaths, US births, Saugeen, temperature rain and the KDD cup 2018.
MOIRAI (Woo et al., 2024) was introduced alongside the LOTSA dataset collection, which aggregates the entire Monash repository. This includes the training portions of M1, M3, M4, and Tourism datasets. While the authors report zero-shot results on long- mor-horizon collections such as ETT, Electricity, and Weather, these results confounded by the fact that Traffic (also part of their long-horizon evaluation) is included in LOTSA pre-training. The MOT TRAT method the most affected by deviations from zero-shot, they pretrain using 76% of the evaluation datasets.
TimesFM (Das and Weather from the pre-trains on the full M4 dataset, as well Electricity, Traffic, benchmark suite. Consequently, its reported results on these datasets should not be interpreted as zero-shot. At the time of this publication, the T TimeFFM model is the least affected by deviations from the zero-shot regime, using only M4 and Weather.
2024)
While yet published, the I22--2 pre-train datasets mentioned here.
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D METRIC DEFINITIONS
In this section, we describe several metrics used in our evaluation.
To ensure the comparability of work with the existing literature, evaluate the accuracy of the forecasts using scaled Continuous Ranked Probability Score (sCRPS, (Gneiting & Raftery 2007)).
defined
sCRPS (y, x) Eie, CRPS( VEA..
(10)
Ei,, [Vi.r.al
That is, the sCRPS is a scaled version of the CRPS in which we divide by the sum of the absolute values of the series. We Riemann integral approximation technique that uniformly averages the quantile loss over discrete set of quantiles:
CRPS(y, Y) x) =2 2
f f (o'
(11)
We complement the evaluation of the probabilistic forecasts through the Mean Absolute Scaled Error (MASE, (Hyndman & Koehler 2006)), that considers the ratio between mean absolute error of forecasts over mean absolute error of the LeasonalNainee ve forecast Dr,c, (i.e., point forecast using the last observation on the previous season), defined as:
Eie, lyi.en Di,th MASE (y, y) Exe, lur.en 11.
(12)
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E TRAINING METHODOLOGY AND HYPERPARAMETER SETTINGS
In this section, we describe more detail our training methodology and hyperparameter settings.
E.1 TRAINING METHODOLOGY
We train the following zero-shot models on our proposed simulator. We consider NBEATS, MLP (basically a single block of NBEATS), and PatchTST. These models represent very different classes of models based on distinct inductive biases (fully-connected design vs. attention- patching design). Moreover, these are time-tested and generally accepted as strong basclines in forecasting literature. Models are implemented in Py PoTchc Paszke et al. 2019) using pytorch lightning framework FFacoon & The Py'Torch Lightning team (2019) trained for 250K (NBEATS) and 500K (PatchTST) steps using the Adam optimizer Kingma & Ba (2013) with default settings and learning rate 0.0001. Batch size is fixed 4096 and the model takes the history of 4096 points (the maximum history length reported in the literature) and predicts 512 horizons ahead in one shot. NEEATS is trained on VxV100 machine, and training takes about 16 hours. PatchTST is trained on 8xA100 machine, and training takes about 48 hours.
Trained models are applied inference time with no tuning of parameters or hyperparameters on test datasets. Hyperparameter settings of the neural networks are provided in Tables 6 and Hyperparameter settings of the proposed SarSim0 simulator are provided in Table 9
To train the networks, we take the simulator generated sequence of length 6000 samples and randomly choose start and end points of the training sequence of total length 4096 (history) plus 512 (forecast length). We then supply history sequence to the neural network and compute the multi-horizon multi-quantile loss (T) against the forecast ground truth, learning with backpropagation. In order to train the networks to deal with variable sequence length, the 4096-length window is zeroed out on the left with padding mask to simulated the effects of padding (the length of zeroed segment sampled uniformly from Uniform [0, 4088). At inference time, short sequences are left padded to length 4096. The output of the network cut to match the required prediction length (specified by the target dataset). For datasets in GiftEval requiring output lengths longer than 512, downsample the input by a factor and upsampled the forecast by the same factor (resulting in output length 1024, which is then trimmed to required forecast length). Downsampling and upsampling are implemented using Kaiser window with filter length 3, rolloff 0.9 from torchaudio Resample function (Yang et al. 2021..
E.2 HYPERPARAMETER SETTINGS
Hyperparameter settings for various models are given in the following tables.
Table 6: NBEATS Hyperparameter Settings
Hyperparameter
Value
Batch Size
4096
Learning rate
0.0001
Training steps
250,000
Input length
4096
Ouput length
512
Main Activation Function
ReLU
Number of Blocks
10
Layers within block
3
Block hidden size
1024
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Table 7: PatchTST Hyperparameter Settings
Hyperparameter
Value
Batch Size
4096
Learning rate
0.0001
Training steps
500,000
Input Length
4096
Output Length
512
Main Activation Function
ReLU
Patch Length
64
Patch Stride
32
Number of Layers
12
Number of Attention Heads
8
d model
512
FFN hidden hidden_size
2048
Apply Revin
True
Residualized Attention
True
Table 8: Chronos-Small Hyperparameter Settings
Hyperparameter
Value
Batch Size
1024
Learning rate
0.0001
Training steps
500,000
Input Length
512
Output Length
512
Main Activation Function
ReLU
Patch Length
Patch Stride
Number of Encoder Layers
6
Number of Decoder Layers
6
Number of Attention Heads
8
use_reg eee_reg_toker token d model
True
512
d ff d
2048
64
Dropout
0
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Table 9: Sarsimo Hyperparameter Settings
Hyperparameter
Value
History Sequence Length
4096
Padding Length
Uniform[0,400) 4088
Forecasting Horizon
512
SARIMA Sampling Configuration
Base Sequence Length
6000
Vectorization Batch Size
256
(AR order)
Uniform 0. 10]
g. (MA order)
Uniform 0..3
P. (Seasonal AR order)
Uniform 0,
Q, (Seasonal MA order)
Uniform (0,
(Seasonality period)
Uniform (0, 52)
F Maxx (AR max pole radius)
0.9
AR pole angle
Uniform[0, 2m]
Rmax (Seasonal AR max pole radius)
0.1
Seasonal AR pole angle
Uniform (0, 2x]
(Non-scasonal integration order)
Uniform 00, 1]
D (Seasonal integration order)
SARIMA-2 Sampling Configuration
Seasonality pairs
Uniform [24. [24, 71, [7, 52), [0, [0, [0, 24), 52]]
@ (Modulation depth)
Uniform 00, 1]
Additive vs. Multiplicative mixing selection probability
0.5
Noisers Sampling Configuration
Input selection probability (SARIMA vs. SARIMA-2)
0.5
Noiser selection
Uniform
QuisormnPPisson, [Poisson, Gamma, Lognormal, Passthrough)
Xo (Base rate for Poisson)
LogUniform(O..I 1. 100]
X6 (Base rate for Generalized Gamma)
LogUniform(0.I 1, 100]
A (Base rate for Lognormal)
LogUniform(0.1, 5]
KP
(Shape for Poisson)
N/A
G
(Shape for Generalized Gamma)
LogUniformm[, 50.0]
kL (Shape for Lognormal)
LogUniform! 1, 3.0]
< (Power for Generalized Gamma)
Uniform[0.5, 1.5]
E.3 SARSIMO HYPERPARAMTER VALUES AND SELECTION METHODOLOGY
The settings of SarSime iim0 simulator parameters appear in Table 9 and the detailed explanation for each setting provided below.
Vectorization Batch Size is set to 256 for on-the-fly generation efficiency.
Model orders p. 9. P. Q are set to values often encountered in practice, e.g., 0, 1, 2, 3, with the exception of p. maximum AR order, set to 10, mostly to demonstrate the efficiency of simulator even with higher-order models that are typically more compute hungry. Smaller settings of this parameter yield similar results.
The seasonality period parameter, 8, was chosen to cover the typical seasonalities encountered the data: yearly data typically have seasonality 0 (no seasonality). monthly data often exhibit seasonality 12, quarterly- 4, hourly- 24, weekly- 52, daily 7. Overall, in order to avoid any benchmark specific biases, decided sample seasonalities in SARIMA uniformly in the range covering most common seasonalities: [0, 52].
Similarly, SARIMA-2 was added using the prior knowledge that many practical time series have double seasonalities, with specific motivating examples from the literature laid out at the beginning of Section 4.2. Hourly data with double seasonality often have 24 7 pattern (within day and within
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week daily patterns); daily data often have 7 x 52 pattern (within week and within year weekly patterns). Additionally, mixing the seasonality process with the typical natural frequencies listed above, in SARIMA-2, enriches the data with the traces that imitate stochastic-ollatiityy patterns through non-linear pross-modulation. These motivate the choice of SARIMA-2 seasonality pairs, uniformly sampled from this set: [24, 7]: [7, 52], [0, 7]. [0, 4), [0, 24], 52].
Next, AR max pole radius is chosen to be 0.9 to avoid any numerical issues due to near-unit-root instability that may arise in AR process due to floating quantization error accumulation effects. Similarly, Seasonal AR max pole radius is set to 0.1 for the same reason. Recall that with seasonality
8 = 24 the seasonality pole will be 0. 1/14 = 0.89, for example. AR pole angles are sampled uniformly in [0, 2m) -noominformttive prior*.
Non-seasonal integration order is sampled uniformly in [0, 1] inn-informattie prior*.
Seasonal integration order is set to 1. We have tried higher integration orders for both, but they didn't work well because of numerical stability issues in long sequences, so we limit the maximum integration order to 1.
SARIMA-2 Modulation depth is sampled uniformly in [o, 1] * *non-informative prior*.
Additive vs. Multiplicative mixing selection probability is set 0.5 "non-informative prior".
Input selection probability (SARIMA vs. SARIMA-2) is set to 0.5 "non-informative prior*.
Noiser selection is motivated by the review of relevant literature at the beginning of Section 4.3, documenting the heteroscedassicctty. intermittency, and heavy-tailed disturbance effects in real data from multiple unrelated application domains. Poisson, LogNormal and Generalized Gamma processes seem to be the dominating and heavy-tail distribution families that cover a variety of real data. This why those were chosen, along with a pass-through (no noise) noiser instance. This list is, of course, non-exaustive, and we believe multiple other noise models are viable and should be explored in future work. The sampling of noisers follows a *non non-inforrattiv uniform prior*.
Base rate for Poisson is sampled from LogUniform[0.11 100] for the following reason. First, for large values of rate À > 100 Poisson is largely indistinguishable from Gaussian. Second, for very low rate values the Poisson noise produces mostly zeros; for example, with X = 0.1, only roughly 1 in 10 samples is non-zero and we decided not to go beyond that. LogUniform distribution used for rate sampling to concentrate more significant Poisson Noiser mass in a significantly non-Gaussian region of the rates.
Base rate for Generalized Gamma is sampled from LogUniformm0.1, 100), inheriting the range from Poisson.
Base rate for Lognormal is sampled from LogUniform(0.1, 5]. where the upper bound is adjusted to 5 to avoid numerical issues. The mean of Log-Normal process is exp(A + o²/2). which explodes quickly if either À or a are larger than 5-10. The shape of Generalized Gamma is sampled from LogUniform[1, 50.0]. The upper bound is set to 50 as the distribution converges to Gaussian for large shape. Alternatively shape below 1, Gamma density blows up near O, producing lot of very small positive values, clustered very close to 0, and a long right tail (cf. the Poisson low-rate zero-dominated case). Shape for Lognormal is sampled from LogUniform[ 1, 3.0], where adjust the upper bound to 3. so that mean of the process is limited by a reasonable number, exp(5 + 3 32/2) se 13360, also effects of rate and variance 32/ /2 4.5 are roughly equal; whereas the lower bound corresponds to the LogNormal with unit variance.
Finally, Power for Generalized Gamma sampled from Uniform[0.5, 1.5] so that Ç = (standard Gamma) sits in the middle, while the interval explores moderate range of heavier-tailed (ç < 1) and lighter-tailed (S 1) shapes. For smaller values of Ç, the density again blows up near zero; whereas for larger values we have observed some numerical issues arising from taking significant power of a large number.
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F FORECASTPEN AND KERNELSYNTE SYNTHETIC GENERATORS
In this section, we provide detailed implementation and analysis of two synthetic time series gener- ators used in recent foundation models: ForecastPFN's ETTS-based generator (Dooley et al. 2023) and Chronos's s KernelSynth GP-based generator (Ansari et al. 2024). Both methods generate diverse training data, but they employ fundamentally different mechanisms structured multiplicative decom- position versus compositional Gaussian processes. We present their mathematical formulations, our optimized implementations, and empirical comparisons of computational efficiency and scalability.
ForecastPFN ETS Generator. ForecastPFN Dooley et al. (2023) generates synthetic training data using a structured prior based on a multiplicative Trror-Trend-Toe Seannd--ssnnlltty (ETS) decomposition. Each series is modeled the product of trend, a multi-scale seasonal component, and a Weibull- distributed noise factor, with all underlying parameters drawn from prior distributions to create the synthetic training corpus. The formal composition is given by the following: The component periods are set to standard values (e-g., Pweek = 7, Pmonth = 30.5). Parameters for trend are drawn from Gaussian priors, while Fourier coefficients for seasonality normalized to unit sum-of-squares. Crucially, the model trains on the noise-free targets (b(t) rather than the full series yt, accelcrating convergence while maintaining generalization noisy real-world data. Here are the details:
scaled Cf.u, dr,v AO, 1/f) and
= (t( 24 = trend(t) scasonal(t) Z4,
21 = + Mmnise (z - 2), ~ Weibull(1,R) == = trend(t) 1 + Mija t + Cim) (Mexp coxp); scasonaly(t),
scasonal(t)
II
ME (weck.month,year)
[r./2]
seasonal,()) = + my
Σ
2r sfn
+ dy cos 2x ):
Per
Pv
with Pweek
7, Pmonth
30.5, Pyear 365.25,
E(oto-
We compared the official ForecastPFN implementation against our optimized vectorized implementa- tion using 50,000 synthetic time series samples to ensure mathematical equivalence. All statistical tests (Kolmogorov-Smimoy negligible effect sizes (Cohen's 's d < 0.01), confirming statistical equivalence between implementa- tions. Our optimized vectorized implementation achieves 14.6x average speedup with 86.8% time reduction while maintaining statistical equivalence to the original implementation.
Mann-Whitne U) show no significant differences (p > 0.05), with
Table 10: Statistical Comparison: Official vs. Our Vectorized Implementation (n=50,000)
Metric
Official y + o
Our Impl. fa + Fo
KS p-value
MW p-value
Cohen's d
Range
20.56 36.66
20.91 + 37.97
0.648
0.888
0.009
Mean
0.85 + 11.14
0.94 + 11.37
0.579
0.243
0.008
Std Deviation
5.22 = 9.08
5.29 9.35
0.894
0.871
0.008
Trends
0.006 0.222
0.008
0.227
0.458
0.206
0.009
Seasonality
13.13 + 3.55
13.14 = 3.55
0.803
0.724
0.004
Noise Level
2.33 + 4.30
2.36 4.46
0.336
0.799
0.006
KernelSynth. KernelSynth is GP-based synthetic time series generator that inverts the Automatic Statistician: rather than discovering kernel compositions to explain data, it randomly composes kemels produce diverse temporal patterns (Ansari et al. 2024 Duvenaud et al.) 2013). The method maintains a kernel bank IC capturing fundamental patterns Linear (trends), Periodic (seasonality at buuly/weekymmonntllyyyent scales), RBF (smooth local variations), Rational Quadratic (multi-scale structures), Constant (bias), and White Noise (stochastic components). Generation proceeds by sam- pling ((11) J} kernels with replacement and hierarchically combining them via random binary
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Efficient Time Series Generators
Generators Computational Complexity
Generation Time (seconds)
80
Generation Time (seconds)
60
10a
1014
Sequence Length
Sequence Length
SARIMA (Ours)
SARIMA2 (Ours)
Forrecst@FN(OOttimisee))
ForecastPFN
KemelSynth
Figure 4: The time per time-series comparison of different simulators.
operations (+ or x) into composite covariance R(I, l'), where addition superposes independent patterns and multiplication creates localized interactions (e.g.. RBFx Periodic yields locally periodic patterns that decay). Finally, length-4syn time series is drawn from the GP prior GP(O, R). We now detail the mathematical formulation of these three core components, The generation pipeline consists of the following elements:
o2: White Aw o Linear k tt'; RBF kRaF exp(-Att /2 Rational-Quadie ARD (1 At? (2all) Periodic kper
Kernel bank K: Constant le
exp( - sin' 2 (mAt/p//e3) with periods p
{4, 6, 12, 24, 26, 30, 48, 52, 60, 96, 365, 730) LENGTHH.
Compositional grammar: Sample ~ (11 kernels Ni, .i,.... from K;; fold recur- sively via random E [+, x} to get R = (((K) K2)) KK)) ...). Addition superposes independent effects; multiplication localizes/gates patterns.
GP sampling: Grid f..m (n 1024), build covariance Kij a(t t,), draw x K).
Table 11: Comparison of synthetic time series generation methods Scales with Length On-the-fly Synthesis
Method
Generalization
ForecastPFN
KernelSynth
X
SarS im0 (ours)
The time per time-series comparison of different simulators is presented in Figure 4 We note that the KernelSynts generation speed is very slow compared to other alternatives. For F ForecastPFN were able achieve comparable speed via vectorization of the original code.
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G UMAP VISUALIZATION ANALYSIS
In this section, we provide more details on our visualization analysis.
The UMAP visualization in Figure of the main paper demonstrates significant and impressive overlap between the synthetic data generated by the SARIMA simulator and the real-world M4- monthly time series. Here, we describe principled and automated methodology to move beyond visual inspection, systematically identifying and characterizing the real-world patterns that the samples SARIMA simulator do not cover.
G.1 METHOODOLOGY
To identify these missing patterns, we employ a two-stage pipeline that first learns a low-dimensional representation of the time series, e.g., through UMAP, and then density-based algorithm to score and rank real series based on their novelty with respect to the synthetic distribution.
Dimensionality Reduction with UMAP and DensMAP. To maintain consistency with the main paper, our initial analysis uses Uniform Manifold Approximation and Projection (UMAP). As a complementary approach for more robust analysis, also use its density-preserving variant, DensMAP (Narayan et al. 2020). While UMAP is powerful for visualizing cluster structures, its assumption of uniform point distribution on the manifold can distort local density information. DensMAP refines this by adding density-preed preservation term to its objective function, producing an embedding that more faithfully represents the local densities of the original data space, which critical for the subsequent novelty detection step. Our DensMAP results are not presented here to manage the document size, but results were qualitatively similar.
Novelty Detection with Local Outlier Factor (LOF). We use the LOF algorithm (Breunig et al., 2000) for density-based novelty detection. For each embedding method (UMAP and DensMAP), an LOF model is trained exclusively the embeddings of the synthetic series. This model learns the density patterns of the "normal" data as defined by the SARIMA sampler. Each real series then scored by this model, where more negative score indicates that the series lies in low- density region of the synthetic data manifold and is thus considered novel. The high-level approach of combining dimensionality reduction with outlier detection is well-established technique for identifying anomalous time series. While our method learns embeddings directly from raw time series, [Hyndman al. (2015) have successfully used feature-based approaches. Furthermore, Vaidya & Vaidya (2022) provides empirical evidence that dimensionality reduction can preserve or even enhance the performance of outlier detection algorithms, supporting the validity our pipeline.
We use default values for the hyperparameters of the LOF model. Series with lowest 5% novelty score are considered as "novel."
G.2 ANALYSIS OF M4-MONTHLY SERIES
Novelty Detection with LOF. We apply our novelty detection pipeline to the M4-monthly dataset across four experimental settings, varying both the dimensionality reduction technique (UMAP vs. DensMAP) and the synthetic data source (basic SARIMA vs. the full Sa im0 simulator). We supplement the analysis on the samples of the full Sars im0 because they are the actual samples feed into the model during training.
In total there are four sets experiments, each of which are demonstrated by two figures:
1. Identifying Novel M4-monthly Series with UMAP/DensMAP and LOF. The left panel shows the 2D embedding space, visualizing the coverage of the M4-monthly dataset by synthetic samples. Real-world series are categorized as covered by the synthetic distribution (green), novel (orange), or among the top-200 most novel (red stars). The right panel displays the same M4-monthly embeddings, colored by their LOF novelty score, highlighting that the most novel series (red) form distinct clusters at the edges of the synthetic data distribution.
2. Visualization of the Top 100 Most Novel M4-monthly Series. This figure visualizes the time series corresponding to the 100 lowest LOF novelty scores from the UMAP/DensMAP analysis.
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Novelty
*
USAP Waaeeaa
*
-5
Fnd muric coachhycch otlert
-20
UNAT Disessioo
USAM Stoendan
Figure Baseline SARIMA + M4-monthly
UMAP. LOF novelty detection results.
SARIMA UMAP. See Figure and Figure
SarSimO + UMAP. See Figure 7 and Figure 8
Our findings be summarized in two key points:
First, the combination of dimensionality reduction and the LOF algorithm is an effective pipeline for systematically identifying simulator coverage gaps. Across both UMAP and DensMAP embeddings, the LOF novelty scores align with visual inspection: the series that form distinct, uncovered clusters in the embedding space precisely those that receive the highest novelty scores. This confirms that the "holes" are not mere visualization artifacts, but instead represent statistically significant deviations from the synthetic data distribution.
Second, consistent and interpretable pattern emerged from the top-ranked novel series across all four experimental settings. These typically correspond time series windows with: (i) abrupt level shifts or structural breaks (i.e., trend slope change or more generally generating process change); (ii) strong, isolated spikes or outages that do not repeat seasonally (especially isolated aperiodic negative spikes); or (iii) patterns with pronounced quasi-periodic calendar effects that are not captured by purely seasonal period-basee SARIMA specification.
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13.20
10.25
1255
Mill
MI
Mil
MI
15.00
Myy
Figure 6: Baseline SARIMA + M4-monthly + UMAP. Top 100 novel M4-monthly series visualization
UMAP with Novelty Detection (LCF)
LOF Novolty Soore Heatmap
1.
Pacl world coverd)) Selcced 2o
*
65
36-
25-
25-
60-
0.-
UMPP treveecee
10VS3 Dinomrionn
Figure 7: SarSim0 + M4-monthly + UMAP. LOF novelty detection results.
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MI
Wi
I'M Morty
Mran 10.00
11
No
Vi
Figure 8: SarSim0 M4-monthly UMAP. Top 100 novel M4-monthly series visualization
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Duffing
Lorenz
Lotka- Volterra
Pendulum
MSE
MAE
MSE
MAE
MSE
MAE
MSE
MAE
Chronos-Large
0.709
0.524
59.2
5.3
2c-4
0.011
0.079
0.174
Chronos-Base
0.671
0.487
57.1
5.1
3e-4
0.011
0.020
0.070
Chronos-Small
0.516
0.432
44.3
4.6
5e-4
0.014
0.150
0.250
Chronos-Mini
0.640
0.548
66.7
6.1
6e-4
0.016
0.849
0.638
Chronos-Tiny
0.798
0.581
57.7
5.5
2e-3
0.026
2.700
1.100
TimesFM
0.718
0.564
77.2
6.1
9e-5
0.006
0.807
0.533
NBEATS-SarSimo 0.609
0,550
56.0
5.7
4e-4
0.014
0.375
0.445
Chronos-SarSim(
0.650
0.510
63.2
5.8
4e-5
0.003
1.220
0.672
PatchTST-SarSim 0.750
0.550
55.1
5.6
4e-5
0.004
0.294
0.366
Table 12: Zero-shot forecasting performance on four nonlinear dynamical systems (Duffing, Lorenz, Vakka-Voltera, Pendulum), reported MSE and MAE for each system.
H ADDITIONAL RESULTS
In this section, we describe additional empirical results based on non-linear dynamical systems.
H.1 NON-LINEAR SYSTEMS RESULTS
To probe the behavior well outside the target regime of traditional statistics based time series, additional zero-shot experiment on four canonical nonlinear dynamical systems (Duff- ing, Lorenz, Lotka- Volterra, Pendulum), comparing several Chronos variants, TimesFM, and NEEATT//PcchTST/Chrree
models trained on SarSimo. We generated datasets for the four non-linear dynamical systems. For each dynamical system, we simulated a single long trajectory of 20,000 time steps. The initial 16,000 steps treated as burn-in, and the final 4,000 steps used for forecasting evaluation. Evaluation results appear in Table [2] while the data-generation procedure for each system summarized below.
Across the four canonical nonlinear systems we explored, the error levels of Sars S m-p-petraiied models are generally in the same range as those of the real-data foundation models. We see this as evidence that, on nonlinear dynamical systems far from our intended application domain and including aperiodic/chaotic behavior, pretraining on SARIMA- models that behave reasonably and on similar scale to models trained on real data. This suggests that the inductive biases used to construct the simulator are not overly restrictive: while they clearly favour series dominated by trend, seasonality, and intermittency, they remain compatible with the level of out-of-domain generalization observed in real-data- paeerraaeeeaieeddddeeeeeeee models.
synthetic family still yields
Pendulum. We consider nonlinear simple pendulum described by its angular displacement and angular velocity. Each trajectory is initialized with random starting angle and angular velocity, and then evolved forward in time using the standard equations of motion under gravity. The physical system is point mass m attached to a massless rigid rod length I, moving in a vertical plane under constant gravitational acceleration g. The dynamics of the pendulum governed by the following second-order differential equation:
0"(1) + sin()(()) 0,
(13)
where:
(t) is the angular displacement of the pendulum at time f,
(t) is the angular acceleration,
is the acceleration due to gravity (9.81 m/s?),
is the length of the pendulum (set to 1.0 m).
The system is further characterized by its initial conditions:
the initial angle dg. which is randomly chosen from a uniform distribution between -7 and æ, and
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the initial angular velocity wa, which is randomly chosen from uniform distribution between - -1 rad/s and rad/s.
The motion of the pendulum is modeled using numerical methods, specifically the Euler method, which approximates the solution of the system of equations over discrete time steps.
Duffing Oscillator. We consider a nonlinear oscillator with damping and a cubic restoring term. For each run, sample random initial displacement and velocity, and we then evolve the system under a periodic external forcing. The underlying dynamics follow the Duffing oscillator, a canonical nonlinear second-order system used model oscillators with nonlinear stiffness and damping. Its evolution is governed by the differential equation:
+ du + az + Fxxx = cos(wi),
where r(f) denotes the oscillator's s displacement, y(t) =(t) its velocity, and the time variable. The system parameters are fixed to a 1.0 (linear stiffness), 8 = 5.0 (nonlinear stiffness), 0.3 (damping coefficient), = 8.0 (driving force amplitude), and w = 0.5 (angular frequency of the driving force). The oscillator is subject to a periodic external drive, and its evolution reflects the combined effects of the nonlinear restoring force and damping. We simulate the dynamics by numerically integrating the equations of motion with a simple time-stepping scheme, where time step and the initial conditions for and y drawn random from small interval. For this choice of parameters, the resulting motion exhibits chaotic behavior.
Lotka- Volterra. We also include predator-pre prey population system, in which prey and predator counts evolve through their mutual interaction. Each trajectory starts from randomly chosen initial population levels, and the dynamics then propagated forward according to the classical Lotka- Volterra equations. The governing equations for the Lotka- VolterVoleera predator-prey model are given by:
d. d.prryy oz. OxNprey
B BNNepyy-Vppedaaaee Npreciator
d. d.N prodator
8NN prey Npreciator 7NN prediators
dt
where:
N pry is the population of the prey species,
Predutor is the population of the predator species,
a is the natural growth rate of the prey,
3 is the predation rate (rate at which predators kill prey),
6 the rate at which predators increase due to consuming prey,
y is the natural death rate of the predator.
In this formulation, the prey population grows exponentially when predators are absent, while the predator population decays exponentially if prey available. Their interaction leads to characteristic cyclical oscillations in both population sizes.
We simulate the system by numerically integrating the differential equations with a simple Euler scheme. At the start of each run, prey and predator populations are initialized at random within prescribed interval. The parameters the populations at every time step.
1.1, 3 = 0.4, 0.1, and 7 0.4 are then used to update
Lorenz '63. We also consider a chaotic dynamical system with three state variables æ, y. and 2. Each trajectory is initialized from random starting conditions and then evolved forward in time using the Lorenz equations under standard parameter settings. The equations governing the Lorenz system are given by:
dr dt
σ =x)
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GvftEval
M-SERIES
sCRPS
MASE
sCRPS
MASE
NBSATSSSSax3im0-4dfaall
0.602
0.849
0.096
0.869
NBEATS-SSar:3m00-p3
0.603
0,851
0.097
0,876
NBEATS-Sar:31m0-p=7
0.600
0.846
0.096
0.867
1BEA4TS-Sar:3im0-=115
0.599
0.850
0.097
0.869
NBEAATS-Saar31m0-p=200
0.602
0.852
0.097
0.872
NBGATSS-Sar31mm00-mm = 0.8
0.601
0.848
0.096
0.870
NBCATTS-Sax::im00>>mm. = 0.95
0.600
0.847
0.097
0.873
NBEATS-SSarSim00-Rm... 0.2
0.601
0.844
0.096
0.869
NBBATSS-Sar:3m00A44.. = 0.5
0.598
0.846
0.096
0.866
NBEATTS-SarS1m00-pp
0.604
0.848
0.097
0.875
NBEATS-Sar:Sim--02
0.602
0.851
0.097
0.871
Table 13: Study of the sensitivity of NBEATS-SarSimo simulator hyperparameters.
dy rlp 2)
dt
dz
xy B2, dt
where:
x, y, and represent the state variables of the system, typically interpreted as the variables
describing the convection rolls the atmosphere,
a is the Prandtl number, a measure of the fluid's viscosity, set to 10.0,
p is the Rayleigh number, representing the temperature difference between the top and bottom of the fluid, set 28.0,
3 is geometric factor, set to
For this choice of parameters, the Lorenz system displays chaotic dynamics: even tiny perturbations the initial state can evolve into drastically different trajectories over time. our experiments, we integrate the system of differential equations using the Euler method over finite sequence of time steps.
H.2 SARSIMO HYPERPARAMETER SENSITIVITY ANALYSIS
In our evaluation, we varied several simulator hyperparameters: the maximum AR order p, the AR pole radius bounds Tmax and Rmaxx scasonal and non-scasonal MA orders (g, Q) around the default configuration, retraining NBEATS-SarSim under the same protocol. Results are summarized in Table 13 Across all these variants, performance both GiftEval and the M-Series remains very similar to the default configuration. This indicates that SarS im0 is not brittle "sweet spot": the configuration we use appears relatively benchmark-agnosti and robust substantial hyperparameter changes, rather than being reliant on finely tuned settings.
H.3 DETAILED GIFTEVAL RESULTS
H.3.1 GIFTEVAL DOMAIN SPLIT
and We report GiftEval results stratified by domain in Tables 14 15 (see Table and its discussion for model and baseline details). An important contextual point is that the Econ/Fin subset of Gvl essentially the M4 competition data, which we show in Appendix CeanuddxxcCaabba (Table to be included in the pretraining corpora of Chronos, MOIRAI, and TiMe Consequently. on Econ/Fin these foundation models are not in strict zero-shot regime, whereas ierSim0--preree never see these series during training and therefore operate under strict zero-shot conditions. Even in this favorable setting for the real-data models, their accuracy advantage Econ/Fin relatively
backbones
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Econ/Fin
Energy
Hcalthcare
Nature
Sales
Transport
Web/CloudOps
Chronos-Base
0.798
0.733
0.513
0,451
0.444
0.594
0.824
Chronos-Small
0.810
0.753
0.525
0,472
0.449
0.614
0.797
MOIRAI-Large
0.778
0.732
0.565
0,382
0,445
0,451
0.748
MOIRAI-Small
0.834
0.763
0.744
0,413
0.442
0.551
0.777
ITM-R2-Pretrainee
1.316
0.944
1.375
0,506
0.765
0.750
1.055
TimesFM
0.761
0.783
0.690
0,411
0.421
0.591
0,935
NBEATS
1.027
1.088
0.755
0.656
0.507
0.688
0.722
PatchTST
0.854
0.712
0.609
0,428
0.426
0.535
0,553
AutoARIMA
0.873
0.969
0.603
0.811
0.561
0.884
1.144
NBFATS-KermelSynth
0.985
0.827
0.609
0,489
0.517
0.649
0.739
NBEATS-ForrcasPPFN
3.640
1.459
2.211
0.603
0.462
0.866
1.174
RatchhST-KKemelSyntt
0.955
0.782
0.586
0,479
0.518
0.605
0.754
PatchhSST-FonecasPFFN
3.904
1.751
3.029
0.656
0.515
1.141
1,333
NBEATS-SarSimo
0.845
0.718
0.516
0.413
0.420
0.556
0.641
PatchTST-SarSimo
0.821
0.687
0.511
0.380
0.417
0.546
0.596
MLP-SarSimO 0.878
0.745
0.655
0.431
0,425
0.597
0.710
Table 14: nCRPS on GiftEval, weighted aggregation by domain. Lower values are better.
Econ/Fin
Energy
Healthcare
Nature
Sales
Transport
Web/CloudOps
Chronos-Bas
0.783
0.924
0.644
0,823
0.726
0.712
1.140
Chronos- Smalll
0.797
0.948
0.607
0,852
0.733
0.737
1.144
MOTRAT-Large
0.845
1,026
0.699
0.750
0.711
0.601
1.125
MCTRAT-Small
0.985
1.069
0.848
0.807
0.731
0.731
1.136
ITM--R--Pretrinee
1.409
1.016
1.176
0,851
0.977
0.792
1,254
TimesFM
0,824
1.017
0.698
0.880
0.701
0.741
2.394
NBEATS
0.861
1.185
0.690
0,933
0.705
0.730
0,916
PatchTST
0.907
0.983
0.685
0.916
0.691
0.709
0.780
AutoARIMA
0.866
1.011
0.783
1.018
0.813
0.973
1.615
NBEATS-KemelSynth
1.013
1.131
0.705
0.975
0.803
0.846
1.033
NBEATS-ForecastPFN
6,009
2.066
2.229
1.134
0.769
1.165
1.688
PatcchrsT-KernelSytth
1.020
1.072
0.699
0.936
0.805
0.793
1.012
PatcchTsT-ForecasPPFN
6.266
1.993
2.744
1.110
0.821
1.338
1.919
NBEATS-SarS1mo 0.830
0.965
0.620
0.817
0.688
0.718
0,918
PatchTST-SarSiim
0.844
0.945
0.665
0.797
0.690
0.708
0.891
MLP-SarSimO 0.985
1.004
0.777
0.858
0.695
0.767
0.976
Table 15: nMASE on GiftEval, weighted aggregation by domain. Lower values are better.
modest, with SarS im0 models trailing only slightly behind. On the remaining six domains (i.e., excluding Econ/Fin), SarS caresimm--riine models provide either very comparable or clearly better accuracy. In terms of sCRPS, SarSime backbone achieves the best score (Energy, Healthcare, Nature, Sales), and is close the best method on Transport and Web/CloudOps. For nMASE, Sa rS m0 best out of domains (Sales, Web/CloudOps), and it typically remains within small margin of the strongest model in the others. Overall, this pattern suggests that the inductive biases of SarSim0 are not tuned to any single domain, but generalize robustly across diverse application areas.
of domains
second observation from Tables 14 15 the uniform dominance of SarSimo over other synthetic generators. Fixing the backbone (N-BEATS or PatchTST) and varying only the pretraining corpus, SarSimo consistently outperforms both KernelSynth and ForecastPFN across GiftEval domains and for both nCRPS and oMASE. For example, NBEATS-SarSine and PatchTST-SS rS mm0
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frequency
10S
10T
15T
5T
A
D
W
Chronos-Base
1.442
0.546
0.833
0.712
0.984
0.476
0.562
0.854
0.850
0.621
Chronos-Small
1.331
0.629
0.859
0.711
1.014
0,500
0.569
0.823
0.856
0.614
MOIRAI-Large
1,464
0.566
0.809
0,480
0.758
0.473
0,497
0.786
0.749
0.726
MOIRAI-Sman
1.638
0.590
0.809
0.551
0.766
0.483
0.552
0.985
0.803
0.788
TTM-R22-Peerainee
2.255
0.511
0.951
0.755
1.436
0.789
0.688
1.495
1.416
1.354
TimesFM
2.177
0.528
0.853
0.701
0.853
0.520
0.570
0.737
0.863
0.689
NBEATS
1.003
0.791
1.070
0.728
0.977
0.660
0.730
0.968
0.983
1.112
PatchTST
0.899
0.498
0.729
0.544
0.853
0.494
0.495
0.837
0.844
0.763
AutoARIMA
1.678
1.149
1.059
1.042
0.948
0.590
0.903
0.764
0.832
0.837
NBFATS-KermelSynt
1.149
0.545
0.823
0.674
1.259
0.556
0.658
0.829
0.950
0.761
NBEATS-ForrcasIPFN
2.142
0.823
1.425
1.001
2.940
0.909
1.013
1.518
3.061
1.500
PatchhST-KeemelSyttt
1.151
0.504
0.797
0.688
1.272
0.554
0.604
0,825
0.957
0.784
PatchhSST-ForecasPFFN
3.349
1.017
1.537
1.112
3.171
0.968
1.154
2.191
2.716
2.276
NBEATS-SarSimo
1.153
0.501
0.718
0.576
0.963
0.470
0.546
0.713
0.827
0.649
PatchTST-SarSimo
1.114
0.440
0.702
0.530
0.998
0.455
0.507
0.755
0.821
0.656
MLP-SarSimO
1.408
0.534
0.743
0.616
1.211
0.482
0.570
0.840
0.912
0.716
Table 16: nCRPS on GiftEval, weighted aggregation by frequency. Lower values are better.
strictly better than their KernelSynth- and ForecastPFN-prerriine counterparts in Econ/Fin, Energy. Healthcare, Nature, Sales, Transport, and Weh/CloudOps.
third comparison is with the non-zero-shot NBEATS and PhTST baselines that are fully supervised each GiftEval dataset. For NBEATS, SarSimo0 mr-pretrained NBEATS strietly improves over dataset-specific NBEATS on all seven domains in nCRPS and on 6 of 7 domains in nMASE (the remaining Web/CloudOps gap is negligible), despite never seeing real data during pretraining. For PhTS. Pat chtTSSSaSaa Simo matches or improves upon the supervised Pat chTTT baseline on the majority of domains (5/7 in nCRPS and 6/7 in nMASE). with only Web/CloudOps (and slightly Transport in nCRPS) still favouring in-domain supervised training.
Overall, this stratified view shows that much the benefit usually attributed to per-dataset supervised training can instead be recovered from a single, domain-agnosse SarSing Aim0 curriculum, with only narrow slice of domains where additional task-specific fitting still offers an advantage.
H.3.2 GIFTEVAL FREQUENCY SPLIT
We further stratify GiftEval by sampling frequency in Tables T6 17 pretraining corpora of Chronos, MOIRAI, Time TimesFM, and TTM include large portions of the M4 competition data, whose dominant frequencies are annual (A), quarterly (Q), and monthly (M). In fact, the Annual and Quarterly splits in GvftEval consist exclusively of M4-yearly and M4-quarterly, respectively. The Monthly split aggregates five datasets (Car Parts, Hospital, M4-monthly, Saugeen, US Births), several which are also used in pretraining: Hospital, Saugeen, US Births, and Car Parts appear in MOIRAI 's pretraining corpus, and Saugeen and US Births in TTM 's. Thus, at A/Q/M frequencies, foundation models operate in regime where their pretraining distribution is especially close to the test distribution, whereas SarS meessiim-pprrraa -ees--mm-rrreeeeed pretrained models never see these series and are evaluated in strict zero-shot setting.
As detailed in Appendix C
Despite this strong advantage for real-data- penert-eee models at A/Q/M, SarSimO backbones remain highly competitive (in fact, best on Monthly split) and are often best other frequencies. For the sub-hourly and minute-level frequencies (10T, 15T, 5T), Pat nCRPS on 1OT and 15T and among the top performers on ST, outperforming both foundation models and per-dataset supervised NBEATS in several cases. At daily (D) frequency, NBEATS- SarSimo and Pat PatchhsT-SarrS imo slightly improve over the best real-data foundation models in nCRPS, while also yielding strong mMASE, indicating that the synthetic curriculum transfers well to operationally important daily horizons. For the weekly bucket (W), GiftEval aggregates eight datasets: Electricity, ETT1, ETT2, Hierarchical Sales, M4-weekly, Saugeen, Solar, and US
imo attains the best
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Published as a conference paper at ICLR 2026
10S
10T
15T
5T
A
D
W
Chronos-Base
2,481
1.088
0.887
0.862
0.918
0.714
0.791
0.857
0.768
0.762
Chronos-Small
2.479
1.204
0.919
0.872
0.943
0.737
0.802
0.827
0.774
0.746
MOIRAI-Large
2,486
1.125
0.984
0.672
0.749
0.727
0.792
0.825
0.712
0.931
MOIRAI-Small
2.419
1.161
0.986
0.773
0.751
0.752
0.899
1.016
0.774
0.968
ITM-R2-Pretrained
2,933
0.917
0.905
0.863
1.294
0.981
0.883
1.207
1,265
1.225
TimesFM
3.733
1.274
0.956
2.380
0.845
0.746
0.855
0.800
0.874
0.847
NBEATS
1.284
1,213
1.016
0.884
0.794
0.775
0.905
0.851
0.755
1.083
PatchTST
1.063
1.189
0.877
0.786
0.830
0.749
0.803
0.859
0.824
0.929
AutoARIMA
4.744
1.001
0.978
1.000
0.935
0.882
1.060
0.759
0.799
0.947
NBFATS-KermelSynt
1.784
1.146
0.958
0.874
1.268
0.888
1.003
0.846
0.923
0.924
NBEATS-ForccastPFN
3.844
1.794
1.765
1.261
3.317
1.317
1.648
1.685
3,996
2.011
PatchhST-KeemelSyutt
1.760
1.103
0.939
0.858
1.274
0,867
0.907
0.841
0.935
0.986
PatchhSST-ForecasPFFN
5.423
1.811
1.529
1.409
3.719
1.362
1.566
2.152
3.781
2.855
NBEATS-SarSimo
1.830
0.996
0.842
0.757
0.944
0.746
0.818
0.746
0.800
0.807
PatchTST-SarSimi
1.712
0.989
0.828
0.744
0.989
0.737
0.791
0.800
0.802
0.837
MLP-SarSimO 1.961
1.110
0.864
0.800
1.312
0.763
0.868
0.897
0.947
0.891
Table 17: nMASE on GiftEval, weighted aggregation by frequency, Lower values are better.
Births. As summarized in Appendix C this segment is heavily represented in the pretraining corpora of the real-data foundation models: Electricity, M4-weekly, and Solar are used to pretrain used by TimesFM; and M4-weekly, Solar, Saugeen, and US Births are used by MOTRAI. In other words, weekly-series evaluation is favorable to these models, whose pretraining distributions backbones remain strictly zero-shot on all eight datasets. Even in this regime, SarSine Sarm models competitive: in nCRPS, NBEATS-SarSime and PawchhsT-SarSinm (0.649 and 0.656) trail only Chronos-Base/Smine (0.621/0.614), and outperform TimesFM, MO I IRAI. A similar pattern holds for nMASE, where NBEATS-San SerATT-Sariimm and Pat chttssasSSrrrsii imm (0.807 and 0.837) sit just behind
Chronos; Electricity and M4-weekly
very close to the test distribution, whereas Sa SarSime warrSimmpppettti mmD-pretrained
This supports the view that SarS imo does not rely on any single "sweet spot" frequency, but instead it transfers robustly even in settings where foundation models benefit from substantial pretraining overlap with the evaluation datasets.
When we move attention to synthetic pretraining only, SarSimo shows a consistent advantage over KernelSynth and ForecastPFN for every frequency bucket. The best synthetic model in terms or
of both nCRPS and nMASE is always either NBEATS-SarS gap is especially pronounced at coarse resolutions (A, Q, M) and at frequencies. This suggests that on forecasting tasks represented in GiftEval, the SARIMA based simulator provides more robust and broadly useful synthetic curriculum than either KernelSynth or ForecastPFN.
The sub-hourly/minute
Finally, compare SarS SarSimm-prees -rr-pretraieed models to the strong per-dataset supervised baselines, NEEATS and Pat chTST. Both SarSing models achieve lower nCRPS than per-dataset counter- parts on out of 10 frequencies (10T, 15T, ST, retain small edge, which we see as natural given their direct access to the target train split. Over- all, this comparison reinforces that single GarSimo --ssed pretraining run can match or exceed carefully tuned per-dataset training across wide range of frequencies.
M. W). At a few regimes, supervised models
H.3.3 GIFTEVAL TERM SPLIT
In Tables 18 19 we further stratify GiftEval by term length: long (including horizons 720, 900). medium (including horizons 480, 600), and short (including horizons 6, 8, 12, 13, 14, 18, 30, 48, 60). Before discussing the results, it is important to note that, among these three strata, the short- term split is the most affected by pretraining overlap. contains 28 datasets, of which six are the M4 competition subsets (daily, hourly, monthly, quarterly, weekly, yearly) used to pretrain all real-data foundation models (Chronos, MOIRAI, TimesFM, TTM), as documented in Appendix In addition, Chronos three more short-term datasets (Solar, KDD Cup 2018, Electricity);
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Published as a conference paper at ICLR 2026
long
medium
short
Chronos-Base
0.721
0.748
0.596
Chronos-Small
0.746
0.743
0,607
MOIRAI-Large
0.598
0,605
0,597
MOIRAI-Small
0.626
0.636
0,666
ITM-R2-Pretrained
0.774
0.816
0,939
TimesFM
0.742
0.748
0.635
NBEATS
0.809
0.805
0.823
PatchTST
0.527
0.548
0.628
AutoARTMA
1.152
0.990
0.808
NBRATS-KemmelSnth
0.667
0.710
0.710
NBEATS-ForecasPPFN
0,994
1.056
1.270
PatchIST-KermdSynttt
0.646
0.666
0.696
FatchTSST-oncccsPFFN
1.137
1.257
1,517
NBEATS-SarSimo
0.574
0.601
0.612
PatchTST-SarSimo
0.538
0.561
0.592
MLP-SarSimO
0.601
0.641
0.660
Table 18: nCRPS on GiftEval, weighted aggregation by term length. Lower values are better.
long
medium
short
Chronos-Base
1.040
1.041
0.768
Chronos-Small
1.078
1.048
0.780
MOIRAI-Large
0.985
0.961
0.807
MOIRAT-Small
1.035
1.021
0.888
TTM-R2-Pretrained
1.043
1.036
1,005
TimesFM
1.623
1.447
0.823
NBEATS
1,056
1.036
0.863
PatchIST
0,881
0,859
0.833
AutOARIMA
1,615
1.026
0.935
KBEATS-Kemnelynthh
1.069
1.101
0.925
NBEATS-
1.676
1.660
1.729
PatchIST-KemedSynth
1.022
1.001
0,912
PatcchTsT-ForeccssPPFN
1,681
1.666
1.879
NBEATS-SarSimo
0.923
0.907
0,802
Pat.chTST-SarSim0
0.896
0.876
0.801
MLP-SarSimO
0.959
0.955
0.871
Table 19: nMASE on GiftEval, weighted aggregation by term length. Lower values are better.
MOIRAI sees twelve more (Car Parts, Covid Deaths, Hicrarchical Sales, Hospital, Jena Weather, KDD Cup 2018, Loop Seattle, Saugeen, Solar, SZ-Taxi, Temperature Rain, US Births); and TimesFM sees Jena Weather and Electricity. Consequently, substantial fraction of the short-term evaluation split consists of datasets that foundation models have already seen during pretraining, whereas SarSimo models see none of them. Despite this favorable overlap for the real-data models, on short- term nCRPS Sa rS m0 -n-pptrraieed backbones (PatchTST TST-Sa r m0: 0.592, NBEATS-Se rS m 0.612) outperform all foundation models, and short-term nMASE they only slightly behind Chronos. Across long and medium terms, which are much less affected by lcakage, SarSim0- pretrained models noticeably ahead of the foundation models.
When we move attention to synthetic-onle only pretraining, Sax farsimo sim0 clearly dominates the other syn- thetic baselines across all term lengths. In Tables [8 19 NBEATS- and Pat TSr-SarS achieve lower nCRPS and nMASE than their KernelSynth and ForecastPFN counterparts in three splits (long, medium, and short).
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Published as a conference paper at ICLR 2026
multivariate
univariate
Chronos-Base
0.685
0.627
Chronos-Small
0.684
0,647
MOIRAI-Large
0.635
0.572
MOIRAI-Small
0.640
0.659
TTM-R2-Pretrained
0.833
0.907
TimesFM
0.717
0.652
NBEATS
0.790
0.837
PatchTST
0.556
0.613
AutoARTMA
1.032
0.826
NHFATS-KemellSynhh
0.700
0.700
NBEATS-ForecasIPFN
1.113
1.194
PatcchIST-KeemelSnttt
0.683
0.674
PatchTTST-ForecasPEEN
1.217
1.501
NBEATS-SarSimo
0.594
0.607
ParchIST-SarSime
0.546
0.595
MLP-SarSimO
0.628
0.655
Table 20: nCRPS on GiftEval, weighted aggregation by variate type. Lower values are better.
H.3.4 GIFTEVAL VARIATE TYPE SPLIT
multivariate
univariate
Chronos-Base
1.013
0.780
Chronos-Small
1.026
0.797
MOIRAI-Large
1.023
0.773
MOIRAI-Small
1.021
0,890
TTM-R2-Pretrained
1.072
0.980
TimesFM
1.497
0,829
NBEATS
0.998
0.892
PatchTST
0.906
0.805
AutCARIMA
1.318
0.912
NBBATS-KemedSynth
1.098
0.914
NBEATTS-ForecastPFN
1.802
1.627
ParcchTSTT-KemeSynttt
1.049
0.885
PatchIesT-ForecasPPPy
1.740
1,825
NBEATS-SarSiim
0.943
0.781
PatchrST-SarSim0
0.904
0.788
MLP-SarSimO
0.979
0.854
Table 21: nMASE on GiftEval, weighted aggregation by variate type. Lower values are better.
The univariate split contains 20 datasets (Car Parts, Covid Deaths, Electricity, Hierarchical Sales, Hospital, KDD Cup 2018, Loop Seattle, M-Dense, M4 Temperature Rain, US Births). As detailed in Appendix C and Section H.3.3 large fraction of these are used in pretraining the real-data foundation models (all overlapping datasets are univariate). In contrast, the multivariate split provides much cleaner zero-shot testbed: to the best of our knowledge, there is no pretrain-test leakage in this segment.
We next stratify GiftEval by variate type (Tables
Restaurant, Saugeen, Solar, SZ.-Txxi,
Against this backdrop, SarSimo SarSim0-pretrainee -pretrained backbones highly competitive the univariate split: Pat
(0.595) and NBEATS-SarS sim0 (0.607) lie close to the leading MOIRAI- Large (0.572) in nCRPS. In nMASE, Lorg again leads (0.773), with SREATS-SarSimd
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Published as a conference paper at ICLR 2026
GiftEval
M-SERIES
sCRPS
MASE
sCRPS
MASE
AutOARIMA
0.912
1.074
0.096
0.843
NBEATS-SarSim0
0.602
0.849
0.096
0.869
No SARIMA-2
0.655
0.913
0.104
0,941
No Noisers
0.609
0.856
0.096
0.860
SarimaOnly
0.672
0.940
0.101
0.891
Table 22: Extended ablation simulator components, including an additional SARIMA- row TIBEATS-Sarimanii trained solely on pure SARIMA samples, without Noisers or SARIMA-2. On GiftEval, this SARIMA-only student already substantially outperforms the practical per-series baseline AutOARIMA in both sCRPS and MASE.
(0.781) and PatchTST-SarSimg (0.788) essentially matching the best real-data models and im- proving over the per-dataset PatchTST/NBEATS baselines (0.805/0.892)).
The picture is even more interesting on the multivariate split, where pretrain-test overlap is much less pronounced. Here, PatchIsT-SarS (0.635), Chronos-Base (0.685), TimesFl: (0.717), and the per-dataset Pat ChTST baseline (0.556). Across both variate types, Sars S 1errmim0ppp -n-eterraieeed models consistently outperform their KernelSynth and ForecastPFN counterparts. Taken together, these results indicate that univariate SARIMA- based simulator can support strong generalization not only to unseen univariate series, but also to multivariate benchmarks, without explicitly modelling cross-series structure.
attains the best nCRPS (0.546), ahead of MOIRAI- -Large
H.4 ADDITIONAL ABLATION COMPARING SARIMA-ONLY CASE AND AU AOTORRIMA
We define cleaner experiment here to study the relationship between AutOARIMA and the gen- cralization models trained on SarSim0 and its components. particular, Table 22 presents an additional row, in which we study the accuracy of NBEATS trained exclusively SARIMA process (row SarimaOnly) without the use of Noisers or SARIMA-2. The conclusions remain aligned with previous observations. On GiftEval, even the SARIMA-only student substantially outperforms AutoARIM IMMM (0.672/0.91 vs. 0.940/1.077 SCRPS/MASE) despite being trained essentially the same model family. On the M-Series, the picture is more mixed, as before: Aut CARIMA remains better in MASE (0.843 vs. 0,869/0.891), while sCRPS is comparable. This is consistent with our discussion that the classical M-Series are particularly favorable per- series ARIMA/ETS-yyR models and with our original characterization of this phenomenon as early, domain-dependent evidence rather than universal effect.
Sarimaanll)
38


Reviews:
[{"review_id": "zRdl3YPTRk", "reviewer": "Reviewer_jA3h", "summary": "The authors propose a scalable synthetic time-series generation pipeline based on a seasonal autoregressive integrated moving average (SARIMA) model. Their proposed simulator follows a three-step procedure that samples traces from the “polynomial stability region”, then combines multiple paths into rich multi-seasonality traces, then adds noise to capture burstiness and intermittency. They show that their simulator allows for strong zero-shot generalization.", "questions": "1. Regd the second set of rows in Table 1: What is NBEATS, PATCHTST and AutoARIMA trained on here? It should be made clear in the table.\n2. Suggestion: can the authors bold the best numbers in each column, say in Table 1, 2 etc.? It is difficult to spot which models are the best", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "- The work is well-motivated. The authors point out how training with real series can be limited by licensing barriers, data scale, domain etc. And that training with synthetic data offers unique levers that can be controlled.", "weaknesses": "- There is very limited analysis conducted with the experiments. First, GIFT-Eval allows for easy analysis of performance stratified by domain/frequency/term length/ variate type etc. These are more important to understand the limitations and strengths of the model, more than the aggregate score on GIFT-Eval. \n\n- To further improve the evaluation, I would suggest adding one of the foundation model baselines (e.g. Chronos) trained from scratch on KernelSynth/ForecastPFN/SarSim0.\nThen it would allow for apples-to-apples comparison with the pretrained Chronos.\n\n- There is no analysis on how this dataset can be used to complement other datasets, which is important to understand. I suggest the authors combine GIFT-Eval train (or a different training set) with this training dataset.\n\n\n**Final verdict**: I give a score of 6 as I see this as a paper that can be accepted. Conditional on addressing the weaknesses and answering questions, l might consider upgrading my score to 8 (if I am satisfied with the answers).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "DcF8sTSpcJ", "reviewer": "Reviewer_GRvF", "summary": "This paper introduces SarSim0, a novel, scalable, and computationally efficient pipeline for generating synthetic time series data for zero-shot forecasting. The core of the simulator is the classical SARIMA statistical model, but with a key innovation: instead of sampling unstable model coefficients, it samples stable poles directly from the characteristic polynomial's stability region, guaranteeing well-behaved series. The pipeline enriches these base signals through a compositional \"SARIMA-2\" scheme for multi-seasonality and adds realism with heavy-tailed noise models to capture burstiness. The authors demonstrate that training standard neural architectures (NBEATS, PatchTST) exclusively on this synthetic data, generated on-the-fly, achieves state-of-the-art zero-shot performance on established benchmarks. Notably, these relatively small models outperform massive, real-data pretrained foundation models and, in many cases, even surpass the forecasting accuracy of the \"teacher\" model (AutoARIMA) from which the data-generating process is derived.", "questions": "Based on my concerns listed above, I pose the following questions to the authors:\n\n*   **Question 1:** The SarSim0 pipeline is built on a SARIMA core, which is fundamentally a linear process model. How do you see this limiting the simulator's ability to generate data with complex non-linear dynamics (e.g., regime shifts, GARCH effects), and could this explain why models pre-trained on it might struggle on certain real-world domains not covered by the benchmarks?\n\n*   **Question 2:** Table 8 shows a large number of hyperparameters for the SarSim0 pipeline. How were these settings chosen? Could you provide an ablation or sensitivity analysis on key parameters, such as the maximum pole radius (`rmax`) or the range of AR/MA orders, to demonstrate the robustness of the approach?\n\n*   **Question 3:** The \"student-beats-teacher\" finding is compelling. However, the effect appears mixed on the M-Series, where AutoARIMA's MASE is stronger than NBEATS-SarSim0. What properties of the M-Series datasets might explain why AutoARIMA remains more competitive there, and does this suggest limits to the emergent generalization?\n\n*   **Question 4:** The ablation study shows that removing the Noisers can sometimes *improve* performance on the M-Series. This suggests a mismatch between the noise model and the real-data characteristics. Does this finding point to a need for more adaptive or domain-specific noise generation, and how might that be incorporated into the pipeline?\n\n*   **Question 5:** The current work focuses on univariate time series. What are the primary conceptual and technical hurdles to extending the SarSim0 methodology, particularly the stable pole sampling approach, to the multivariate case where capturing cross-series dependencies (e.g., via a VARIMA framework) is essential?\n\n*   **Question 6:** The UMAP visualization in Figure 3 shows impressive overlap. However, are there any noticeable \"holes\" or regions in the real-data embedding space (red) that the synthetic data (blue) fails to cover? What kind of real-world patterns might these correspond to, and do they align with the known limitations of SARIMA models?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "*   **Core Technical Problem:** The primary strength of this work is its novel and principled solution to the instability problem in autoregressive model simulation. By shifting from sampling coefficients to directly sampling the poles of the transfer function within the unit circle (Section 4.1), the authors guarantee the generation of stable, non-divergent time series. This is a technically sound and elegant idea that makes the powerful but notoriously fragile SARIMA framework a viable engine for large-scale data generation. The resulting speed and on-the-fly capability (Figure 4) represent a significant practical advantage over slower, more complex methods like kernel-based synthesis.\n\n*   **State-of-the-Art Zero-Shot Performance from Synthetic Data Alone:** The paper's empirical results are strong and challenge a key assumption in the field. Table 1 shows that a standard PatchTST model trained solely on SarSim0 data not only outperforms prior synthetic-only methods by a massive margin but also achieves the best overall scores on the GIFT-Eval benchmark, surpassing large foundation models like Chronos, MOIRAI, and TimesFM that were pre-trained on vast amounts of real data. This is a landmark result, demonstrating for the first time that a purely synthetic corpus can be a viable—and even superior—substitute for real-world data in zero-shot forecasting.\n\n*   **Demonstration of Emergent Generalization (\"Student-Beats-Teacher\"):** A deep and significant finding is that neural models trained on SarSim0 data consistently outperform their own data-generating \"teacher,\" AutoARIMA, on the GIFT-Eval benchmark. This is not trivial. It suggests that by learning from a vast and diverse *distribution* of SARIMA processes, the neural network is not merely fitting the teacher's behavior but is learning a more fundamental and robust representation of time series dynamics. This emergent capability is a powerful argument for the synthetic-first pre-training paradigm.\n\n*   **Methodology:** The authors demonstrate a commitment to rigorous, leakage-free evaluation. They operate under a strict zero-shot protocol and provide a detailed breakdown in Appendix C (Table 5) of how prior foundation models violate this protocol by pre-training on evaluation data. This meticulous approach adds significant credibility to their claims and serves as a valuable contribution to the community by highlighting pervasive issues in model evaluation. The ablation study (Table 2) is also effective in validating the importance of the SARIMA-2 and Noiser components.", "weaknesses": "In my opinion, the paper's reliance on the SARIMA framework introduces inherent limitations, and the scope of its claims could be tempered by a more nuanced discussion of the benchmarks and the simulator's own complexity.\n\n1.  **Inherent Linearity of the SARIMA Core:** The SARIMA model, which forms the backbone of the simulator, is fundamentally a linear process model. While the paper adds complexity via superposition and non-Gaussian noise, it cannot natively generate time series with core non-linear dynamics, such as regime switching, threshold effects, or volatility clustering (GARCH-like effects). Many real-world series, particularly in finance and econometrics, are driven by such phenomena. The paper's success on the chosen benchmarks may indicate that these benchmarks are dominated by seasonal/trend components, but the simulator's applicability to more complex, non-linear domains remains an open question.\n\n2.  **Opaqueness of the Simulator's \"Meta-Tuning\":** The SarSim0 pipeline itself has a large number of hyperparameters that define the distribution of generated series: the ranges for AR/MA/Seasonal orders, the maximum pole radii, the parameters for seasonality pairs, and the distributions for the Noiser module (Table 8). The paper presents a configuration that works exceptionally well, but it provides no insight into how this configuration was determined. The performance of the downstream \"student\" models is critically dependent on the quality and diversity of the \"teacher's\" curriculum, and this meta-level tuning process is a crucial, yet undiscussed, part of the methodology.\n\n3.  **Potential for Overgeneralization from Current Benchmarks:** The evaluation is performed on the M-Series and GIFT-Eval benchmarks, which are excellent but are heavily composed of business, economic, and demographic time series. These are domains where SARIMA-like models have historically excelled. It is unclear if the remarkable performance would transfer to domains with fundamentally different characteristics, such as chaotic physical systems, high-frequency financial data, or irregular biological signals (e.g., ECG). The simulator's strong inductive bias is a feature, but it may also be a limitation.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "VzjZoHBVZ6", "reviewer": "Reviewer_qasc", "summary": "This paper introduces SarSim0, a fast synthetic time‑series generator. The authors train forecast models entirely on simulated data and then test their zero‑shot performance on real datasets from the GIFT-Eval and M4 datasets. The SarSim0 pipeline first samples stable SARIMA processes by sampling AR/MA poles inside the unit circle, then composes bi‑seasonal structure via an additive/multiplicative SARIMA‑2 modulation, and finally overlays level‑dependent heavy‑tailed noise (Poisson, generalized‑Gamma, lognormal) to capture burstiness and intermittency. Because the authors’ approach generates data on‑the‑fly at scale, compact backbones (N‑BEATS, PatchTST, MLP) trained solely on a large set of SarSim0 time series achieve strong cross‑frequency zero‑shot accuracy matching or surpassing larger pretrained models like Chronos. The authors also show that pretraining with their synthetic data leads to stronger results on GIFT-Eval than pretraining with earlier synthetic data sources (PFN and KernelSynth). When comparing to fully-trained models, the authors find that models pretrained on SarSim0 data outperform direct forecasts using AutoARIMA, a phenomenon the authors refer to as “student beats teacher” generalization.", "questions": "1. The unit circle pole requirement acts as a stability condition on the AR process generating the data. Are there any mathematical conditions or theoretical guarantees on the distributional properties of the resulting time series?\n\n2. Can you directly quantify the verisimilitude and diversity of your generated data, particularly compared to prior PFN or structured causal model approaches? For example, since you have a UMAP, you could calculate a silhouette score. A statistical significance test would add depth to this comparison.\n\n3. Are you fine-tuning Chronos, Moirai, etc on the SarSim0 dataset? I could not tell if these experiments are what are shown in the first rows Table 1, or if that shows the base performance of those models pretrained on their original pretraining splits.\n\n4. I am confused by Table 1. Are the three models (lines 387-389) fully-trained on the context? And why are Chronos-Base and others not marked as zero-shot models?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "The SARIMA-2 approach is an appropriate generating model that describes many practical time series. As noted by the authors, many demand or utility time series benchmarks consist of a slow process (like inflation in a financial time series) modulating a fast process (like seasonal demand). Within this generating model class, the authors make appropriate choices to enforces stability in the AR dynamics by sampling poles inside the unit circle. This likely helps preserve diversity in the generated time series.\n\nThe evaluations and experiments are appropriate in scope. The authors use GIFT-Eval, which is the current leading benchmark for zero-shot evaluations. They also perform ablations of each component of their generator, allowing them to identify that SARIMA-2 (biseasonality) is a key driver of their approach.\nI also like the experiment design of comparing fully-trained NBEATS/PatchTST against variants pretrained on prior synthetic data generators (KernelSynth/PFN).\n\nThe authors give a nice demonstration that their generated data co-clusters with real datasets from the M4 competition. Because nonlinear embeddings are neighbor based, this helps show that their data convincingly “passes” as real time series data", "weaknesses": "**Novelty.** This is not the first paper to train a zero-shot forecast model  purely on simulation data and report strong results. ForecastPFN and TabPFN first used this approach, while Mamba4Cast uses an SSM on PFN synthetic data to achieve strong results on the original GluonTS datasets. While the idea itself is not the first of its kind, the arguments in favor of this paper could be (1) the particular choice of synthetic data generation, and (2) the empirical results. I do not currently feel that either is strong enough to recommend acceptance.\n\nAd hoc data augmentation. Regarding the data generation procedure, I consider the approach to be sufficiently ad hoc that it’s hard to see why a SARIMA approach would be universally preferable. There are not any theoretical guarantees or general bounds that establish that this approach will always produce more diverse or realistic data than prior methods. Prior approaches fall broadly into PFN and its variants (as in ForecastPFN/TabPFN), augmentations thereof (as in Mamba4cast, which introduces spike injection and damping augmentation, or Gaussian-process based methods like KernelSynth used by Chronos. There’s also structured approaches like CauKer, which combine Gaussian Processes with a structured causal model. I can see the author’s ARIMA-based procedure as helping cover data types not covered by other methods; for example, long history dependence when the ARIMA process has a long effective memory due to slow damping. However, it’s hard to argue that any of these dataset generators are universally preferable. \n\n**Experiments.** The experiments show that models like NBEATS or PatchTST become competitive with models like Chronos when pretrained on the SarSim0 dataset. I don’t consider these results strong enough to believe that they justify selecting this data generator over others, because I think there is a bit of a “no free lunch” here: the authors pick a generator that handles multiseasonality well, and it turns out this is useful for M4 and GIFT-Eval, which has many time series that fall into that class. But had the authors picked a multi-scale or trend-dominated test set, a different heuristic for data generation approach could have been preferable. Since there are infinite choices that could be made during the data generation procedure, the overperformance of this particular set of choices mainly tells us about the properties of GIFT-Eval and M4.\n\n**Emergence.** I do not agree with the “emergent effect” argument.  A neural model pretrained with SARIMAX datasets outperforming AutoARIMA does not imply emergent effects. Firstly, Sarima-2 does not directly fall within the model class directly expressible by AutoARIMA. Secondly, initialization and hyperparameters can prevent a model like AutoARIMA from exactly fitting the true generator.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "YJNTGk8guh", "reviewer": "Reviewer_gKMt", "summary": "The authors propose a new pipeline to generate synthetic data for the pre-training of time-series foundation models. They show that models trained purely on their synthetic data can outperform leading time-series foundation models trained on real data.", "questions": "* How well do models trained on your synthetic data perform on predicting dynamical processes not described by ARIMA processes? For example, deterministic chaos.\n* I am asking this because SARSIM0 has a very strong inductive bias towards time series with seasonality or bi-seasonality, while chaotic time series are aperiodic. Can the authors comment on how models trained with SARSIM0 fair with aperiodic time series in general?\n* Have you tried train a model with both SARSIM0 data and real data? Will it outperform models trained on either synthetic data or real data alone?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "Being able to generate high-quality synthetic data that fully replace real data is a big deal. This has the potential to overcome the scarcity of real-world time-series data and allow scaling time-series foundation models beyond the current billion-parameter regime.", "weaknesses": "There are some strong inductive bias built into the SARSIM0 process, such as bi-seasonality, which are well suited for the tasks in GIFT-EVAL and M-Series benchmarks but may fail in other application domains, especially in scientific machine learning. See my questions below.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:

Decision: Accept (Poster)