Dynamic covariance matrix models for energy forecasting

Effective management of renewable energy sources depends on accurate forecasts, particularly in a probabilistic format for decision-making under uncertainty. When dealing with multiple forecasts across different locations or times, it's crucial to assess if errors will compound or offset each other.

We introduce a novel approach for modeling the covariance matrix $\boldsymbol{\Sigma}$ of prediction errors $\boldsymbol{Y} = {y_1, y_2, \ldots, y_p}$ associated with different lead times. Our methodology utilizes the modified Cholesky decomposition to model $\Sigma$ without the constraint of positive definiteness. This decomposition allows us to interpret matrix elements in terms of linear regression, revealing smooth patterns that can be effectively captured using a Generalized Additive Model (GAM). This approach not only improves the parsimony of our model but also incorporates temporal variables, allowing for a dynamic estimation of the covariance.