Analysis of High Dimensional Multivariate Stochastic Volatility Models

Washington University, Olin Working Paper No. 98-11

Posted: 18 Aug 1999

See all articles by Siddhartha Chib

Siddhartha Chib

Washington University in St. Louis - John M. Olin Business School

Federico Nardari

University of Melbourne - Department of Finance

Neil Shephard

Harvard University

Date Written: July 1, 1999

Abstract

This paper is concerned with the fitting and comparison of high dimensional multivariate time series models with time varying correlations. The models considered here combine features of the classical factor model with those of the univariate stochastic volatility model. Specifically, a set of unobserved time-dependent factors, along with an associated loading matrix, are used to model the contemporaneous correlation while, conditioned on the factors, the noise in each factor and each series is assumed to follow independent three-parameter univariate stochastic volatility processes. A complete analysis of these models, and its special cases, is developed that encompasses estimation, filtering and model choice. The centerpieces of our estimation algorithm (which relies on MCMC methods) is (1) a reduced blocking scheme for sampling the free elements of the loading matrix and the factors and (2) a special method for sampling the parameters of the univariate SV process. The sampling of the loading matrix (containing typically many hundreds of parameters) is done via a highly tuned Metropolis-Hastings step. The resulting algorithm is completely scalable in terms of series and factors and very simulation-efficient. We also provide methods for estimating the log-likelihood function and the filtered values of the time-varying volatilities and correlations. We pay special attention to the problem of comparing one version of the model with another and for determining the number of factors. For this purpose we use MCMC methods to find the marginal likelihood and associated Bayes factors of each fitted model. In sum, these procedures lead to the first unified and practical likelihood based analysis of truly high dimensional models of stochastic volatility. We apply our methods in detail to two datasets. The first is the return vector on 20 exchange rates against the US Dollar. The second is the return vector on 40 common stocks quoted on the New York Stock Exchange.

JEL Classification: C22

Suggested Citation

Chib, Siddhartha and Nardari, Federico and Shephard, Neil, Analysis of High Dimensional Multivariate Stochastic Volatility Models (July 1, 1999). Washington University, Olin Working Paper No. 98-11. Available at SSRN: https://ssrn.com/abstract=174208

Siddhartha Chib (Contact Author)

Washington University in St. Louis - John M. Olin Business School ( email )

One Brookings Drive
Campus Box 1133
St. Louis, MO 63130-4899
United States
314-935-4657 (Phone)
314-935-6359 (Fax)

Federico Nardari

University of Melbourne - Department of Finance ( email )

Faculty of Economics and Commerce
Parkville, Victoria 3010 3010
Australia

Neil Shephard

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

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