Multivariate electricity load forecasting

The problem

Electricity is difficult to store, so the quantity generated at any moment must match demand as closely as possible. Grid operators rely on short-term load forecasts — typically one hour to a few days ahead — for unit commitment, economic dispatch, and real-time balancing. The problem is inherently multivariate: loads across different regions and building types are correlated, share daily and weekly seasonality, and respond jointly to weather. Treating them as independent series throws away information that can meaningfully improve accuracy.

Data

The primary dataset is ISO New England's multiregional electricity load record — five years of hourly data across six sub-regions of the New England grid (Maine, New Hampshire, Vermont, Connecticut, Rhode Island, Massachusetts), paired with aggregated temperature observations from regional weather stations. Two years serve as the training period for parameter initialisation; the subsequent three years serve as the prediction period, with all four algorithms updated recursively as new observations arrive. Forecast horizons range from one hour to two weeks ahead, evaluated using point metrics (MAPE, RMSE) and probabilistic metrics (log-score, pinball loss across nine quantiles).

Approach

The thesis develops and compares four recursive forecasting algorithms within a unified state-space framework: MAPLF — a novel multivariate probabilistic model generalising Álvarez et al. (2021) to the multivariate Gaussian case, which fuses day-ahead predictions with incoming observations via an inverse emission distribution; the Kalman Filter as a classical baseline; the Inverted State-Space Model, a third novel method that jointly conditions on previous states and current observations; and VAR as an unconditional reference. All parameters are updated recursively with exponential decay, making the models adaptive to non-stationarity without retraining from scratch.

Findings

MAPLF consistently outperforms the Kalman Filter, VAR, and the inverted state-space baseline across both point metrics (MAPE, RMSE) and probabilistic metrics (log-score, pinball loss), with the gap widening at horizons beyond six hours ahead. The advantage is largest for sub-regions with strong cross-regional demand correlation — Rhode Island and Connecticut, whose loads track Massachusetts patterns closely — exactly where exploiting the multivariate structure adds the most information over independent univariate models.

Recursive exponential-decay parameter updates allow all four models to adapt to the seasonal non-stationarity of electricity demand without full retraining. Across the three-year prediction period, MAPLF maintains well-calibrated uncertainty: its probabilistic forecasts are competitive on pinball loss across all nine evaluated quantiles, not only the median.

Code

The full MATLAB implementation — training, prediction, and evaluation pipelines for all four algorithms — is available on GitHub, along with mathematical documentation in a companion Jupyter notebook.

Background

I received my master's degrees in applied mathematics in 2022 from the University of Trento, Italy, supervised by Veronica Vinciotti and co-supervised by Santiago Mazuelas at the Basque Center for Applied Mathematics in Bilbao. You can find the complete thesis here.