Functional Autoregressive Models: An Application to Brazilian Hourly Electricity Load

Abstract

The features of the electrical demand and its response to climate variables impose three main features to the load curves: (1) strong inertia, (2) Each observation is a function and (3) cyclical movements. Based on that, we present a generalization of periodic autoregressive models for functional data with functional covariates. We also estimate a functional autoregressive model, where the periodicity of the parameters is induced by harmonic acceleration operators. Using this method, we handle annual load curves, while the first takes into account the daily load curves. We use splines to represent the smooth functions underlying the points. The estimators of the parameters embody the smoothness restrictions enforced on load curves. We compare the Root Mean Squared Error (RMSE) of our models with the RMSE of a benchmark model. We apply this framework to a dataset from the Southeast/Midwest Brazilian Interconnected Power System, from 2003/01/01 to 2011/01/20.