Density Forecast Transformations

Matteo Mogliani
Banque de France, France
 

Abstract:

The popular choice of using a direct forecasting scheme implies that the individual predictions ignore information on their 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 which ignores the potential dependence. We show the superior performance of our method in empirical examples based on macroeconomic data, where we construct (i) quarterly forecasts using month-on-month direct forecasts and (ii) annual-average forecasts using quarter-on-quarter direct forecasts.

Matteo Mogliani is at Banque de France since 2010, and Head of the International Macroeconomics Division since 2024. He previously covered several positions (including Head of Section and Deputy Head of Division) in the Conjunctural and Macroeconomic Forecasting Directorate. He holds a Ph.D. in Economics from the Paris School of Economics and EHESS. His academic research mainly focuses on time-series econometrics (frequentist and Bayesian), machine learning, macroeconomic forecasting, cointegration, structural breaks, and non-linear time-series modeling. His research has been published in journals including the Journal of Econometrics, the International Journal of Forecasting, and the Journal of Money, Credit and Banking.

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