Real-time macroeconomic forecasting with a heteroskedastic inversion copula

There is a growing interest in allowing for asymmetry in the density forecasts of macroeconomic variables. In multivariate time series, this can be achieved with a copula model, where both serial and cross-sectional dependence is captured by a copula function, and the margins are nonparametric. Yet most existing copulas cannot capture heteroscedasticity well, which is a feature of many economic and financial time series. To do so, we propose a new copula created by the inversion of a multivariate unobserved component stochastic volatility model, and show how to estimate it using Bayesian methods. We fit the copula model to real-time data on five quarterly U.S. economic and financial variables. The copula model captures heteroscedasticity, dependence in the level, time-variation in higher moments, bounds on variables and other features. Over the window 1975Q1–2016Q2, the real-time density forecasts of all the macroeconomic variables exhibit time-varying asymmetry. In particular, forecasts of GDP growth have increased negative skew during recessions. The point and density forecasts from the copula model are competitive with those from benchmark models—particularly for inflation, a short-term interest rate and current quarter GDP growth. Supplementary materials for this article are available online.