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A Fractionally Integrated Wishart Stochastic Volatility Model

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Abstract

There has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of the FIWSV model in order to obtain a closed form expression of moments. We conduct a two-step procedure, namely estimating the parameter of fractional integration via log-periodgram regression in the rst step, and estimating the remaining parameters via the generalized method of moments in the second step. Monte Carlo results for the procedure shows reasonable performances in nite samples. The empirical results for the bivariate data of the S&P 500 and FTSE 100 indexes show that the data favor the new FIWSV processes rather than one-factor and two-factor models of Wishart autoregressive processes for the covariance structure.

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Bibliographic Info

Paper provided by Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico in its series Documentos de Trabajo del ICAE with number 2013-07.

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Length: 29 pages
Date of creation: 2013
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Handle: RePEc:ucm:doicae:1307

Note: The authors are most grateful to Yoshi Baba and Christian Hafner for very helpful comments and suggestions. The 1rst author acknowledges the nancial support of the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science, and Australian Academy of Science. The second author is most grateful for the nancial support of the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science. Address for correspondence: Faculty of Economics, Soka University, 1-236 Tangi-cho, Hachioji, Tokyo 192-8577, Japan.
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Keywords: Difusion process; Multivariate stochastic volatility; Long memory; Fractional Brownian motion; Generalized Method of Moments.;

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