LAUSR

In this letter, the modeling of the multi-seasonal component of the national electric load is investigated. Differently from additive models that consider just the sum of daily, weekly, and yearly periodic components, in order to account for possible interaction terms a full parametrization in the frequency domain is considered. In the case of quarter-hourly data, almost 1 million parameters are needed to specify the model, which motivates the development of efficient learning techniques capable of enforcing sparsity in the parameter space. For this purpose, a Least Absolute Shrinkage and Selection Operator with Fast Fourier Transform (LASSO-FFT) algorithm is devised, having $O{(}n\log {(}n{))}$ complexity. Applied to Italian load data, the LASSO-FFT algorithm yields one-year ahead forecasts whose Mean Absolute Percentage Error (MAPE), is close to one-day ahead predictors currently used by the Italian transmission system operator.