DynLMC: Dynamic Linear Coregionalization for Realistic Synthetic Multivariate Time Series

Synthetic data is essential for training foundation models for time series (FMTS), but most generators assume static correlations, missing realistic inter-channel dependencies. We introduce DynLMC, a Dynamic Linear Model of Coregionalization that incorporates time-varying, regime-switching correlations and cross-channel lag structures. This approach produces synthetic multivariate time series with correlation dynamics that closely resemble real data. Fine-tuning three foundational models on DynLMC-generated data yields consistent zero-shot forecasting improvements across nine benchmarks. Our results demonstrate that modeling dynamic correlations enhances FMTS transferability, highlighting the importance of data-centric pretraining.