Multiforecasting

Multiforecasting is the practice of producing forecasts for multiple related time series simultaneously, exploiting interdependencies among series to improve predictive accuracy and ensure coherency across series and horizons.

It encompasses two broad strategies. The first is joint modeling, where all series are estimated together in a multivariate framework such as vector autoregression (VAR) or vector error correction models (VECM), Bayesian VAR, or dynamic factor models. The second is separate forecasts from univariate models augmented by a reconciliation step to enforce consistency across levels, known as forecast reconciliation (for example, MinT).

Dynamic factor models use a small set of latent factors to capture common movements across many series, providing scalable forecasts for high-dimensional data. State-space and hierarchical models further structure dependencies, while machine learning approaches can produce multi-output forecasts with shared representations.

Key advantages include improved accuracy when series are correlated, coherent forecasts across related series, and the ability to borrow strength from across series when data are sparse. Challenges include high dimensionality, nonstationarity, structural breaks, and computational demands, as well as the risk of overfitting.

Common applications arise in macroeconomics, finance, energy and utilities, retail demand planning, supply chains, and epidemiology, where related variables drift together or influence one another.

Evaluation of multiforecasting emphasizes both accuracy on individual series and coherence across the forecast horizon, using metrics like RMSE or MAE per series, and joint measures such as energy score or the CRPS; cross-validation and backtesting are standard.