  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.
