We construct long-term prediction intervals for time-aggregated future values of univariate economic time series. We propose computational adjustments of the existing methods to improve coverage probability under a small sample constraint. A pseudoout-of-sample evaluation shows that our methods perform at least as well as selected alternative methods based on model-implied Bayesian approaches and bootstrapping. Our most successful method yields prediction intervals for eight macroeconomic indicators over a horizon spanning several decades.
Previous findings indicate that the inclusion of dynamic factors obtained from a large set of predictors can improve macroeconomic forecasts. In this paper, we explore three possible further developments: (i) using automatic criteria for choosing those factors which have the greatest predictive power; (ii) using only a small subset of preselected predictors for the calculation of the factors; and (iii) utilizing frequency-domain information for the estimation of the factor models. Reanalyzing a standard macroeconomic dataset of 143 U.S. time series and using the major measures of economic activity as dependent variables, we find that (i) is not helpful, whereas focusing on the low-frequency components of the factors and disregarding the high-frequency components can actually improve the forecasting performance for some variables. In the case of the gross domestic product, a combination of (ii) and (iii) yields the best results.
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.
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