Multivariate Stochastic Volatility with Co-Heteroscedasticity

This paper develops a new methodology that decomposes shocks into homoscedastic and heteroscedastic components. This specification implies there exist linear combinations of heteroscedastic variables that eliminate heteroscedasticity; a property known as co-heteroscedasticity. The heteroscedastic part of the model uses a multivariate stochastic volatility inverse Wishart process. The resulting model is invariant to the ordering of the variables, which we show is important for volatility estimation. By incorporating testable co-heteroscedasticity restrictions, the specification allows estimation in moderately high-dimensions. The computational strategy uses a novel particle filter algorithm, a reparameterization that substantially improves algorithmic convergence and an alternatingorder particle Gibbs that reduces the amount of particles needed for accurate estimation. We provide an empirical application to a large Vector Autoregression (VAR), in which we find strong evidence for co-heteroscedasticity and that the new method compares favorably to previous ones in terms of forecasting from horizon 3 onward. A Monte Carlo experiment illustrates that the new method estimates well the characteristics of approximate factor models with heteroscedastic errors.