The DC-Cholesky Multivariate Stochastic Volatility Model

Abstract

This paper investigates how the ordering of variables affects properties of the time-varying covariance matrix in the Cholesky multivariate stochastic volatility model. It establishes that estimated covariance matrices, obtained under alternative orderings of variables, are systemically different when the data exhibits independent volatility dynamics. Specifically, simulations show that estimated covariances and correlations become more different, the larger the ratio of individual volatility paths becomes. This paper shows that this property is important for empirical applications as alternative estimates on the evolution of U.S. systematic monetary policy and on inflation-gap persistence indicate that conclusions may hinge on a selected ordering of variables. The dynamic correlation Cholesky multivariate stochastic volatility model is proposed as a robust alternative.