Title: Zero-shot Forecasting by Simulation Alone
Primary area: learning on time series and dynamical systems
Keywords: forecasting, foundation models, simulation, zero-shot

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. We propose the first practical time-series simulation pipeline which is scalable, fast enough for on-the-fly generation, and enables notable zero-shot forecasting performance. Our simulator is based off of a seasonal autoregressive integrated moving average (SARIMA) as its core data source. Due to instability in the autoregressive component, naive SARIMA parameter sampling often leads to unusable paths. Instead, our simulator follows a three-step procedure: (1) we sample well-behaved trajectories from the system's 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 diverse seasonalities and trends. Orders of magnitude faster than kernel-based generators, our simulator enables training on circa 1B unique purely simulated series generated on the fly, after which well-established neural backbones exhibit strong zero-shot generalization, surpassing strong statistical forecasters and recent foundation baselines, while operating under strict zero-shot protocol. Notably, we observe a ``student-beats-teacher'' effect: models trained on our simulations exceed the forecasting accuracy of the generating processes (i.e. AutoARIMA), suggesting emergent generalization beyond the simulator's components.