Zero-shot Forecasting by Simulation Alone

2026-01-02

arXiv.org

AI Summary

Zero-shot time series forecasting in real-world industrial settings is hindered by data scarcity, bias, and privacy constraints. To address this, this work proposes SarSim0—the first zero-shot forecasting framework capable of generating high-quality synthetic univariate time series in real time. Built upon the SARIMA model, SarSim0 synthesizes data rich in trend, seasonality, and intermittency through stability-preserving sampling in the characteristic polynomial space, multi-seasonal path superposition, and rate-based heavy-tailed noise modeling, enabling end-to-end neural network training. Experiments demonstrate that SarSim0 significantly outperforms conventional statistical methods and recent foundation models on the M-Series and GiftEval benchmarks under a strict zero-shot protocol, exhibiting strong generalization. Moreover, it achieves simulation speeds orders of magnitude faster than kernel-based approaches and even exhibits a “student surpassing the teacher” phenomenon, where the trained neural network exceeds the performance of the AutoARIMA process that generated its training data.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Time-Series/Data Streams
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• zero-shot forecasting
• time-series simulation
• data scarcity
• evaluation leakage
• privacy constraints

Innovation

• zero-shot forecasting
• time series simulation
• SARIMA
• heavy-tailed noise
• multi-seasonality