Density forecast transformations

TL;DR

This paper introduces a copula-based method to incorporate cross-horizon dependence into density forecasts, improving accuracy in multi-horizon predictive tasks without changing existing direct forecasting models.

Contribution

The paper proposes a novel copula approach to combine direct density forecasts across horizons, addressing a key limitation in existing methods.

Findings

Copula-based method outperforms traditional approaches in Monte Carlo simulations.

Method improves density approximation in empirical forecast examples.

Enhanced multi-horizon forecast accuracy demonstrated in various empirical cases.

Abstract

The popular choice of using a $direct$ forecasting scheme implies that the individual predictions do not contain information on cross-horizon dependence. However, this dependence is needed if the forecaster has to construct, based on $direct$ density forecasts, predictive objects that are functions of several horizons ($e.g.$ when constructing annual-average growth rates from quarter-on-quarter growth rates). To address this issue we propose to use copulas to combine the individual $h$-step-ahead predictive distributions into a joint predictive distribution. Our method is particularly appealing to practitioners for whom changing the $direct$ forecasting specification is too costly. In a Monte Carlo study, we demonstrate that our approach leads to a better approximation of the true density than an approach that ignores the potential dependence. We show the superior performance of our method in several empirical examples, where we construct (i) quarterly forecasts using month-on-month $direct$ forecasts, (ii) annual-average forecasts using monthly year-on-year $direct$ forecasts, and (iii) annual-average forecasts using quarter-on-quarter $direct$ forecasts.