“Functional factor regression with an application to electricity price curve modeling"

We propose a function-on-function linear regression model for time-dependent curve data that is consistently estimated by imposing factor structures on the regressors. An integral operator based on cross-covariances identifies two components for each functional regressor: a predictive low-dimensional component, along with associated factors that are guaranteed to be correlated with the dependent variable, and an infinite-dimensional component that has no predictive power. In order to consistently estimate the correct number of factors for each regressor, we introduce a functional eigenvalue difference test. Our setting enables us to construct a novel central limit theorem, making it possible to conduct statistical inference on the functional regression parameters. The model is applied to forecast electricity price curves in three different energy markets. Its prediction accuracy is found to be comparable to popular machine learning approaches, while providing interpretable insights into the conditional correlation structures of electricity prices.