SDE-Synth: Stochastic Synthetic Data Generation for Pretraining Time-Series Foundation Models

Time-series foundation models (TSFMs) depend on pretraining corpora that expose the temporal mechanisms they must recognize, yet observational data provide limited control over rare stochastic events, nonstationarity, and cross-series dependence. We introduce SDE-Synth, a hierarchical stochastic-differential-equation-based generator for synthetic univariate and multivariate time series. It simulates configurable latent stochastic dynamics for univariate series and, for multivariate series, shared and variable-specific latent components with controllable cross-series dependence, then maps them to observed data through flexible observation and noise layers. Motivated by financial stylized facts, SDE-Synth targets structural coverage rather than market calibration. Across two TSFM architectures, it improves zero-shot forecasting across all FinStressTS mechanism families under synthetic-only pretraining and consistently improves held-out financial tasks when combined with real data, while GIFT-Eval transfer remains domain-dependent. These results support stochastic synthetic data as a targeted complement to real pretraining corpora.