Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence

Abstract

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this paper, 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.

Real‐time inflation forecast combination for time‐varying coefficient models

“…In the present study, we use real-time data in the forecasting exercise instead of heavily revised data. There has already been much Bayesian work studying real-time macroeconomic variable forecasting, such as forecasts using Bayesian vector autoregressive models (Clark, 2011), forecasts of inflation and the output gap (Garratt, Mitchell, Vahey, & Wakerly, 2011), UK monetary aggregates (Garratt, Koop, Mise, & Vahey, 2009), inflation forecasts by Bayesian model averaging (Groen et al, 2013), and forecasts of macroeconomic variables by a copula model with asymmetric margins (Smith & Vahey, 2016). The present study follows these pioneer studies and employs both Bayesian estimation and real-time data to study inflation.…”

“…The results of the proposed combination forecasts models are highly competitive during the 2007/08 financial crisis. The SPF collects forecasts from professional forecasters and their forecasts are generally quite close to the actual values and difficult to beat (Smith & Vahey, 2016;Tibiletti, 1994).…”

Capturing Macroeconomic Tail Risks with Bayesian Vector Autoregressions

“…This work has emphasized the link of tail risks to output stemming from poor financial conditions. Other work has considered tail risks to other variables, such as unemployment (e.g., Galbraith and van Norden (2019) and Kiley (2018)), or used other methods, such as copula modeling (e.g., Smith and Vahey (2016) and Loaiza-Maya and Smith (2019)) or copula-based combinations of forecasts (e.g., Karagedikli, Vahey, and Wakerly (2019)) to quantify tail risks. Still other work (e.g., Loria, Matthes, and Zhang (2019)) has extended the analysis of Adrian, Boyarchenko, and Giannone (2019a) -henceforth, ABG -to better understand tail risks.…”

Copula modelling of dependence in multivariate time series

“…In this special case the model nests those for multivariate time series employed by Lambert and Vandenhende (2002), Biller and Nelson (2003) and Smith and Vahey (2013).…”