@techreport{oai:grips.repo.nii.ac.jp:00001778,
 author = {CHAN, Joshua and DOUCET, Arnaud and Leon-Gonzalez, Roberto and STRACHAN, Rodney W.},
 note = {http://www.grips.ac.jp/list/jp/facultyinfo/leon_gonzalez_roberto/, First version: October, 2018 [18-12] http://doi.org/10.24545/00001640, 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., JEL Classification Codes: C11, C15, Roberto Leon-Gonzalez acknowledges financial support from the GRIPS Policy Research Center under the grant "Multivariate Stochastic Volatility with Partial Homoscedasticity", from the Nomura Foundation (BE-004) and from JSPS (category C, 19K01588)., Rodney Strachan acknowledges financial support from the GRIPS Policy Research Center for a research visit to GRIPS.},
 title = {Multivariate Stochastic Volatility with Co-Heteroscedasticity}
}