Multivariate Stochastic Volatility with Co-Heteroscedasticity

42 Pages Posted: 22 Oct 2018

See all articles by Joshua C. C. Chan

Joshua C. C. Chan

University of Technology Sydney (UTS) - UTS Business School; Purdue University

Arnaud Doucet

University of Oxford

Roberto Leon-Gonzalez

National Graduate Institute for Policy Studies (GRIPS)

Rodney W. Strachan

University of Queensland - School of Economics

Date Written: October 22, 2018

Abstract

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. That is, these linear combinations are homoscedastic; a property we call 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 impulse response analysis but is generally important for, e.g., volatility estimation and variance decompositions. 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 alternating-order particle Gibbs that reduces the amount of particles needed for accurate estimation. We provide two empirical applications; one to exchange rate data and another to a large Vector Autoregression (VAR) of US macroeconomic variables. We find strong evidence for co-heteroscedasticity and, in the second application, estimate the impact of monetary policy on the homoscedastic and heteroscedastic components of macroeconomic variables.

Keywords: Markov Chain Monte Carlo, Gibbs Sampling, Flexible Parametric Model, Particle Filter, Co-heteroscedasticity, state-space, reparameterization, alternating-order

JEL Classification: C11, C15

Suggested Citation

Chan, Joshua C. C. and Doucet, Arnaud and Leon-Gonzalez, Roberto and Strachan, Rodney W., Multivariate Stochastic Volatility with Co-Heteroscedasticity (October 22, 2018). CAMA Working Paper No. 52/2018, Available at SSRN: https://ssrn.com/abstract=3270662 or http://dx.doi.org/10.2139/ssrn.3270662

Joshua C. C. Chan

University of Technology Sydney (UTS) - UTS Business School ( email )

Sydney
Australia

Purdue University

West Lafayette, IN 47907-1310
United States

Arnaud Doucet

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

Roberto Leon-Gonzalez

National Graduate Institute for Policy Studies (GRIPS) ( email )

7-22-1 Roppongi, Minato-Ku
Tokyo 106-8677, Tokyo 106-8677
Japan

Rodney W. Strachan (Contact Author)

University of Queensland - School of Economics ( email )

Brisbane, QLD 4072
Australia

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