| Purdue Computational Finance Program | |
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Analysis of High Dimensional Multivariate Stochastic Volatility Models
February 25, 2002
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Abstract:
This talk is concerned with the fitting and comparison of high dimensional multivariate time series models with time varying correlations. The model proposed and considered here combines 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 correlations while, conditioned on the factors, the noise in each factor and each series is assumed to follow independent three-parameter univariate stochastic volatility processes. The model includes both heavy-tailed student-t distributions and series-specific jump components, features that are known to be important in financial applications. A unified analysis of this model, and its special cases, is developed that encompasses estimation, filtering and model choice. The centerpieces of the estimation algorithm (which relies on MCMC methods) are (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 tuned Metropolis-Hastings step. The resulting algorithm is scalable in terms of series and factors and simulation-efficient. Methods for estimating the log-likelihood function and the filtered values of the time-varying volatilities and correlations are also provided. Special attention is given to the problems of comparing one version of the model with another and for determining the number of factors. In sum, these procedures lead to the first practical likelihood based analysis of truly high dimensional models of stochastic volatility. The methods are applied in detail to simulated data and to a real data set on returns of 40 common stocks listed on the New York Stock Exchange. |
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2002 Purdue University Last Update: Feb 21, 2002 Please send comments and suggestions to the Webmaster. |