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Matrix-State Particle Filter for Wishart Stochastic Volatility Processes

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  • Roberto Casarin

    ()
    (Department of Economics, University Of Venice Cà Foscari)

  • Domenico Sartore

    (Department of Economics, University Of Venice Cà Foscari)

Abstract

This work deals with multivariate stochastic volatility models, which account for a time-varying variance-covariance structure of the observable variables. We focus on a special class of models recently proposed in the literature and assume that the covariance matrix is a latent variable which follows an autoregressive Wishart process. We review two alternative stochastic representations of the Wishart process and propose Markov-Switching Wishart processes to capture different regimes in the volatility level. We apply a full Bayesian inference approach, which relies upon Sequential Monte Carlo (SMC) for matrix-valued distributions and allows us to sequentially estimate both the parameters and the latent variables.

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Bibliographic Info

Paper provided by Department of Economics, University of Venice "Ca' Foscari" in its series Working Papers with number 2007_30.

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Length: 16
Date of creation: 2007
Date of revision:
Handle: RePEc:ven:wpaper:2007_30

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Keywords: Multivariate Stochastic Volatility; Matrix-State Particle Filters; Sequential Monte Carlo; Wishart Processes; Markov Switching.;

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  1. Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.
  2. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 150(2), pages 167-181, June.
  3. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-488, CIRJE, Faculty of Economics, University of Tokyo.
  4. Michael McAleer & Felix Chan & Les Oxley, 2013. "Modeling and Simulation: An Overview," Working Papers in Economics, University of Canterbury, Department of Economics and Finance 13/18, University of Canterbury, Department of Economics and Finance.
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  6. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
  7. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, Elsevier, vol. 134(2), pages 341-371, October.
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  13. J. Durbin & S. J. Koopman, 2000. "Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 62(1), pages 3-56.
  14. Denis Pelletier, 2004. "Regime Switching for Dynamic Correlations," Econometric Society 2004 North American Summer Meetings, Econometric Society 230, Econometric Society.
  15. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(1), pages 69-87, January.
  16. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 12(4), pages 413-17, October.
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  19. So, Mike K P & Lam, K & Li, W K, 1998. "A Stochastic Volatility Model with Markov Switching," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 16(2), pages 244-53, April.
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Cited by:
  1. Alberto Bisin & John Geanakoplos & Piero Gottardi & Enrico Minelli & Heracles Polemarchakis, 2009. "Markets and Contracts," Working Papers, University of Brescia, Department of Economics 0915, University of Brescia, Department of Economics.
  2. Francesco Menoncin & Paolo Panteghini, 2009. "Retrospective Capital Gains Taxation in the Real World," CESifo Working Paper Series, CESifo Group Munich 2674, CESifo Group Munich.
  3. Alessandra Del Boca & Michele Fratianni & Franco Spinelli & Carmine Trecroci, 2009. "The Phillips curve and the Italian lira, 1861-1998," Working Papers, University of Brescia, Department of Economics 0908, University of Brescia, Department of Economics.
  4. Roberto Casarin & Marco Tronzano & Domenico Sartore, 2013. "Bayesian Markov Switching Stochastic Correlation Models," Working Papers, Department of Economics, University of Venice "Ca' Foscari" 2013:11, Department of Economics, University of Venice "Ca' Foscari".
  5. Alessandro Fedele & Paolo M. Panteghini & Sergio Vergalli, 2010. "Optimal Investment and Financial Strategies under Tax Rate Uncertainty," Working Papers, Fondazione Eni Enrico Mattei 2010.68, Fondazione Eni Enrico Mattei.
  6. Monica Billio & Roberto Casarin, 2010. "Bayesian Estimation of Stochastic-Transition Markov-Switching Models for Business Cycle Analysis," Working Papers, University of Brescia, Department of Economics 1002, University of Brescia, Department of Economics.
  7. Martin Meier & Enrico Minelli & Herakles Polemarchakis, 2009. "Competitive Markets with Private Information on Both Sides," Working Papers, University of Brescia, Department of Economics 0917, University of Brescia, Department of Economics.
  8. Alessandro Fedele & Francesco Liucci & Andrea Mantovani, 2009. "Credit availability in the crisis: the European investment bank group," Working Papers, University of Brescia, Department of Economics 0913, University of Brescia, Department of Economics.
  9. Alessandro Fedele & Raffaele Miniaci, 2010. "Do Social Enterprises Finance Their Investments Differently from For-profit Firms? The Case of Social Residential Services in Italy," Journal of Social Entrepreneurship, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(2), pages 174-189, October.
  10. Rosella Levaggi & Francesco Menoncin, 2009. "Decentralized provision of merit and impure public goods," Working Papers, University of Brescia, Department of Economics 0909, University of Brescia, Department of Economics.
  11. Celik, Nurcin & Son, Young-Jun, 2011. "State estimation of a shop floor using improved resampling rules for particle filtering," International Journal of Production Economics, Elsevier, Elsevier, vol. 134(1), pages 224-237, November.

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