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Multivariate Stochastic Volatility: A Review
Authors:Manabu Asai  Michael McAleer  Jun Yu
Institution:1. Faculty of Economics , Soka University , Tokyo , Japan m-asai@soka.ac.jp;3. School of Economics and Commerce, University of Western Australia , Perth , Australia;4. School of Economics and Social Sciences, Singapore Management University , Singapore
Abstract:The literature on multivariate stochastic volatility (MSV) models has developed significantly over the last few years. This paper reviews the substantial literature on specification, estimation, and evaluation of MSV models. A wide range of MSV models is presented according to various categories, namely, (i) asymmetric models, (ii) factor models, (iii) time-varying correlation models, and (iv) alternative MSV specifications, including models based on the matrix exponential transformation, the Cholesky decomposition, and the Wishart autoregressive process. Alternative methods of estimation, including quasi-maximum likelihood, simulated maximum likelihood, and Markov chain Monte Carlo methods, are discussed and compared. Various methods of diagnostic checking and model comparison are also reviewed.
Keywords:Asymmetry  Diagnostic checking  Estimation  Factor models  Leverage  Model comparison  Multivariate stochastic volatility  Thresholds  Time-varying correlations  Transformations
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