Abstract
Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, and estimate the copula using Bayesian methods. We examine the forecasting performance of the model for four U.S. macroeconomic variables between 1975:Q1 and 2011:Q2 using quarterly real-time data. We find that the point and density forecasts from the copula model are competitive with those from a Bayesian VAR. During the recent recession the forecast densities exhibit substantial asymmetry, avoiding some of the pitfalls of the symmetric forecast densities from the Bayesian VAR. We show that the asymmetries in the predictive distributions of GDP growth and inflation are similar to those found in the probabilistic forecasts from the Survey of Professional Forecasters. Last, we find that unlike the linear VAR model, our fitted Gaussian copula models exhibit nonlinear dependencies between some macroeconomic variables. This article has online supplementary material.
Highlights
A communication issue arises with the forecast densities produced by conventional reducedform macroeconomic models
We aim to demonstrate the potential of the copula framework for modeling and density forecasting using multivariate time series in empirical macroeconomics
Bayesian selection methods have been used in multivariate time series modeling of macroeconomic variables in a number of previous studies (George, Sun and Ni 2008; Korobilis 2010; Jochmann et al 2013), and our study extends these
Summary
A communication issue arises with the forecast densities produced by conventional reducedform macroeconomic models. As Cogley, Morozov and Sargent (2005) emphasize, vector autoregressions (VARs), with or without stochastic volatility, use elliptical disturbances, so that the forecast densities produced are either exactly or approximately symmetric. Some central banks, including the Bank of England and Norges Bank, explore the scope for asymmetric forecast densities as communication tools. The predictive distributions for key U.S macroeconomic variables published by the Survey of Professional Forecasters (SPF) periodically exhibit asymmetries, in particular during the recent recession. In this paper we propose using a copula model to construct asymmetric forecast densities for U.S macroeconomic variables. We aim to demonstrate the potential of the copula framework for modeling and density forecasting using multivariate time series in empirical macroeconomics
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