Quantile Regression for Peak Demand Forecasting

Abstract

We demonstrate that annual peak demand days are characterized by both extreme values of predictors (such as weather) and large unpredictable shocks to demand. OLS approaches incorporate the former feature, but not the latter, leading OLS to produce downwardly-biased estimates of the annual peak. We develop a new estimation procedure, optimal forecast quantile regression (OFQR), that uses quantile regression to estimate a model of daily peak demand, then uses a loss function framework to estimate a quantile to predict the annual peak. We compare the results of the OLS and OFQR estimation approaches for 32 utility zones. While the OFQR approach is unbiased, OLS under-forecasts by nearly 5% on average. Further, OFQR reduces the average absolute percent error by 43%. A bootstrapping procedure generates forecast intervals with accurate 95% coverage in sample and 87% coverage out of sample.