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Multivariate Stochastic Volatility Models with Correlated Errors

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Author Info

  • David Chan
  • Robert Kohn
  • Chris Kirby

Abstract

We develop a Bayesian approach for parsimoniously estimating the correlation structure of the errors in a multivariate stochastic volatility model. Since the number of parameters in the joint correlation matrix of the return and volatility errors is potentially very large, we impose a prior that allows the off-diagonal elements of the inverse of the correlation matrix to be identically zero. The model is estimated using a Markov chain simulation method that samples from the posterior distribution of the volatilities and parameters. We illustrate the approach using both simulated and real examples. In the real examples, the method is applied to equities at three levels of aggregation: returns for firms within the same industry, returns for different industries, and returns aggregated at the index level. We find pronounced correlation effects only at the highest level of aggregation.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 25 (2006)
Issue (Month): 2-3 ()
Pages: 245-274

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Handle: RePEc:taf:emetrv:v:25:y:2006:i:2-3:p:245-274

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Related research

Keywords: Bayesian estimation; Correlation matrix; Leverage; Markov chain Monte Carlo; Model averaging;

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Cited by:
  1. Asai, M. & Caporin, M. & McAleer, M.J., 2012. "Forecasting Value-at-Risk Using Block Structure Multivariate Stochastic Volatility Models," Econometric Institute Research Papers EI 2012-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  2. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility (Revised in May 2007, Handbook of Financial Time Series (Published in "Handbook of Financial Time Series" (eds T.G. Andersen, R.A. Davis, Jens-Peter Kreiss," CARF F-Series CARF-F-094, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  3. Yuta Kurose & Yasuhiro Omori, 2013. "Dynamic Equicorrelation Stochastic Volatility," CIRJE F-Series CIRJE-F-907, CIRJE, Faculty of Economics, University of Tokyo.
  4. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility," CIRJE F-Series CIRJE-F-488, CIRJE, Faculty of Economics, University of Tokyo.
  5. Tsunehiro Ishihara & Yasuhiro Omori, 2009. "Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors," CARF F-Series CARF-F-198, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  6. Jacek Osiewalski & Anna Pajor, 2009. "Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 1(2), pages 179-202, November.
  7. So, Mike K.P. & Choi, C.Y., 2008. "A multivariate threshold stochastic volatility model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 306-317.
  8. Tsunehiro Ishihara & Yasuhiro Omori & Manabu Asai, 2014. "Matrix Exponential Stochastic Volatility with Cross Leverage," CIRJE F-Series CIRJE-F-932, CIRJE, Faculty of Economics, University of Tokyo.
  9. Xiuping Mao & Esther Ruiz & Helena Veiga, 2013. "One for all : nesting asymmetric stochastic volatility models," Statistics and Econometrics Working Papers ws131110, Universidad Carlos III, Departamento de Estadística y Econometría.

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