Keywords: Forecasting, LASSO, Time-series
We construct prediction intervals for a time-aggregated univariate response time series in a ultra high-dimensional regression regime. Additionally we allow a very general form of temporal dependence in the error process. The consistency of our approach is shown for cases when the number of observations is less than the number of covariates, particularly for the popular LASSO estimator. We allow for general heavy-tailed, long-memory, and non-linear stationary process and validate our approach using simulations. Finally, we construct prediction intervals for hourly electricity prices over horizons spanning 17 weeks and compare them to selected Bayesian and bootstrap interval forecasts.