Abstract

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.

摘要

对宏观经济变量的密度预测中的不对称性越来越感兴趣。在多元时间序列中，这可以通过copula模型来实现，其中copula函数同时捕获了序列和截面相关性，并且余量是非参数的。然而，大多数现有的copulas无法很好地捕获异方差，这是许多经济和金融时间序列的特征。为此，我们提出了一种通过对多元未观察到的成分随机波动率模型进行反演而创建的新copula，并展示了如何使用贝叶斯方法对其进行估计。我们使copula模型适合五个季度美国经济和金融变量的实时数据。copula模型捕获了异方差性，水平依赖性，较高时刻的时变，变量范围和其他特征。在1975Q1-2016Q2窗口，所有宏观经济变量的实时密度预测都显示出随时间变化的不对称性。特别是，在经济衰退期间，对GDP增长的预测增加了负偏斜。copula模型的点和密度预测与基准模型的点和密度预测具有竞争力-特别是在通胀，短期利率和当前季度GDP增长方面。可在线获得本文的补充材料。短期利率和当前季度GDP增长。可在线获得本文的补充材料。短期利率和当前季度GDP增长。可在线获得本文的补充材料。