Long-term prediction intervals with many covariates

TL;DR

This paper develops a method for constructing long-term prediction intervals in high-dimensional time series with many covariates, accounting for complex error structures and improving forecast coverage.

Contribution

It introduces a quantile-based approach using LASSO residuals for prediction intervals, with theoretical guarantees and a bootstrap enhancement for better coverage.

Findings

The method performs well with heavy-tailed and nonlinear errors.

Simulation studies validate the theoretical properties.

Application to electricity prices demonstrates practical effectiveness.

Abstract

Accurate forecasting is one of the fundamental focus in the literature of econometric time-series. Often practitioners and policy makers 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 non-linear dependence, are often also influenced by many external predictors. In this paper, 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 process 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.