Long‐term prediction intervals with many covariates

Accurate forecasting is one of the fundamental focuses in the literature of econometric time‐series. Often practitioners and policymakers want to predict outcomes of an entire time horizon in the future instead of just a single k‐step ahead prediction. These series, apart from their own possible nonlinear dependence, are often also influenced by many external predictors. In this article, we construct prediction intervals of time‐aggregated forecasts in a high‐dimensional regression setting. Our approach is based on quantiles of residuals obtained by the popular LASSO routine. We allow for general heavy‐tailed, long‐memory, and nonlinear stationary error processes and stochastic predictors. Through a series of systematically arranged consistency results, we provide theoretical guarantees of our proposed quantile‐based method in all of these scenarios. After validating our approach using simulations, we also propose a novel bootstrap‐based method that can boost the coverage of the theoretical intervals. Finally analyzing the EPEX Spot data, we construct prediction intervals for hourly electricity prices over horizons spanning 17 weeks and contrast them to selected Bayesian and bootstrap interval forecasts.