Long?term prediction intervals with many covariates

Accurate forecasting is one of the fundamental focuses in literature econometric time-series. Often practitioners and policymakers want to predict outcomes an entire time horizon future instead 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 time-aggregated forecasts high-dimensional regression setting. Our approach based on quantiles residuals obtained popular LASSO routine. We allow for general heavy-tailed, long-memory, stationary error processes stochastic Through series systematically arranged consistency results, provide theoretical guarantees our proposed quantile-based method all these scenarios. After validating using simulations, propose novel bootstrap-based that can boost coverage intervals. Finally analyzing EPEX Spot data, hourly electricity prices over horizons spanning 17 weeks contrast them selected Bayesian bootstrap interval forecasts.