Multivariate Forecasting

Multivariate forecasting is the time-series prediction task that simultaneously forecasts multiple co-evolving time series, often incorporating auxiliary covariates that influence the future values. It contrasts with univariate forecasting, which predicts each series independently from its own history. Most real-world forecasting problems are inherently multivariate: retail demand depends on promotions, weather, and correlated product sales; financial risk depends on market indices and macro factors; energy load depends on temperature and calendar effects.

The task has three principal input types: (1) multiple target series that must be jointly predicted, (2) past covariates (features known only up to the forecast origin, e.g., past foot traffic), and (3) future covariates (features known in advance for the forecast horizon, e.g., planned promotional campaigns or weather forecasts). Different model families handle these inputs differently — direct multivariate models like TimesFM-3 natively accept all three, while univariate models like TimesFM-2.5 process each series independently and require per-series covariate engineering.

The transformer era has produced a range of architectures for multivariate forecasting: PRformer (2024, pyramidal recurrent transformer), MTSMAE (2022, masked autoencoder), TwinS (2024, twin-stream for non-stationarity), and FAiT (2026, frequency-aware inverted transformer). The 2026 generation of foundation models (TimesFM-3, Chronos-2) treats multivariate forecasting as a native capability rather than an extension.

Multivariate forecasting is adjacent to time-series-analysis (the broader field), univariate-forecasting (the simpler one-series-per-prediction task), and time-series-foundation-model (the pre-trained-transformer paradigm applied to forecasting). It is distinct from multivariate-regression in targeting time-indexed multi-step prediction rather than cross-sectional point prediction.