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 heteroskedasticity 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 heteroskedasticity, 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