Variable Selection Methods for Probabilistic Load Forecasting: Empirical Evidence from Seven States of the United States

TL;DR: The evidence from the empirical study covering seven states of the United States suggests that: 1) the two methods indeed return different variable sets for the underlying models and 2) HoM slightly outperforms but does not dominate HeM with respect to the skill of probabilistic load forecasts.

Abstract: Variable selection is the process of selecting a subset of relevant variables for use in model construction. It is a critical step in forecasting but has not yet played a major role in the load forecasting literature. In probabilistic load forecasting, many methodologies to date rely on the variable selection mechanisms inherited from the point load forecasting literature. Consequently, the variables of an underlying model for probabilistic load forecasting are selected by minimizing a point error measure. On the other hand, a holistic and seemingly more accurate method would be to select variables using probabilistic error measures. Nevertheless, this holistic approach by nature requires more computational efforts than its counterpart. As the computing technologies are being greatly enhanced over time, a fundamental research question arises: can we significantly improve the forecast skill by taking the holistic yet computationally intensive variable selection method? This paper tackles the variable selection problem in probabilistic load forecasting by proposing a holistic method (HoM) and comparing it with a heuristic method (HeM). HoM uses a probabilistic error measure to select the variables to construct the underlying model for probabilistic forecasting, which is consistent with the error measure used for the final probabilistic forecast evaluation. HeM takes a shortcut by relying on a point error measure for variable selection. The evidence from the empirical study covering seven states of the United States suggests that: 1) the two methods indeed return different variable sets for the underlying models and 2) HoM slightly outperforms but does not dominate HeM with respect to the skill of probabilistic load forecasts. Nevertheless, the conclusion might vary on other datasets. Other empirical studies of the same nature would be encouraged as part of the future work.