Zero-shot Forecasting by Simulation Alone

TL;DR

SarSim0 introduces a fast, leakage-free SARIMA-based simulator that generates on-the-fly synthetic time series with stable poles, double-seasonality, and heavy-tailed noise to enable zero-shot forecasting. The three-stage pipeline—pole-sampled SARIMA, SARIMA-2 modulation, and Noisers—yields diverse, realistic training data at scale, allowing neural forecasters to generalize across GiftEval and M-Series without target data. Across multiple backbones, SarSim0 pretraining matches or surpasses real-data foundation models and outperforms kernel-based synthetic generators, with a notable student-beats-teacher effect on GiftEval. This work demonstrates the viability of synthetic curricula for scalable, privacy-preserving time-series foundation models and highlights avenues for richer volatility and regime-switching extensions.

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 across a variety of domains. Our simulator, which we call SarSim0 (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. SarSim0 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.

Figures (8)

• Figure 1: SarSim0 simulator pipeline. Top: two base components are generated by SARIMA with AR (and seasonal) roots sampled via the characteristic polynomial inside the stability region, yielding well-behaved paths at seasonalities $s\!=\!24$ and $s\!=\!7$. Middle: a SARIMA-2 superposition/modulation 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-gamma bursts, and log-normal volatility capturing burstiness, intermittency, and realistic deviations from Gaussian noise.
• Figure 2: Sampling of SARIMA poles by SarSim0. The SARIMA order-10 AR process poles are shown along with the unit circle on the left. The resulting generated processes with these poles are shown on the right. The top pane shows poles sampled according to the proposed procedure, resulting in a realistic looking time series. The bottom pane shows the result of unconstrained random generation of AR coefficients, resulting in a divergent time series that is useless from the perspective of training time series foundation models.
• Figure 3: SarSim0 Fidelity with Real time series Data. Center: UMAP embedding space of 60-step windows from real dataset M4-Monthly (red) overlaid on equal-length samples from SARIMA simulator with uniformly sampled seasonality $s\in\{0,\dots,24\}$ (blue). Left and right: real (red) and synthetic (blue) series drawn from the circled regions. Key take-aways include: (1) the simulator spans the seasonal regimes seen in real data (e.g., M4-Monthly), including the overall dataset as a special case; and (2) within a seasonality, synthetic series closely match real exemplars co-located in the embedding space, yielding realistic, fine-grained patterns.
• Figure 4: The time per time-series comparison of different simulators.
• Figure 5: Baseline SARIMA + M4-monthly + UMAP. LOF novelty detection results.