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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. 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, vol. 62(1), pages 3-56.
  2. GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor and Francis Journals, vol. 25(2-3), pages 361-384.
  4. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De.
  5. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
  6. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
  7. 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, vol. 16(2), pages 244-53, April.
  8. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
  9. Joan Jasiak & R. Sufana & C. Gourieroux, 2005. "The Wishart Autoregressive Process of Multivariate Stochastic Volatility," Working Papers 2005_2, York University, Department of Economics.
  10. Philipov, Alexander & Glickman, Mark E., 2006. "Multivariate Stochastic Volatility via Wishart Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 313-328, July.
  11. Aguilar, Omar & West, Mike, 2000. "Bayesian Dynamic Factor Models and Portfolio Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 338-57, July.
  12. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
  13. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
  14. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor and Francis Journals, vol. 25(2-3), pages 145-175.
  15. G Sandmann & Siem Jan Koopman, 1996. "Maximum Likelihood Estimation of Stochastic Volatility Models," FMG Discussion Papers dp248, Financial Markets Group.
  16. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
  17. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
  18. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  19. Asai, Manabu & McAleer, Michael, 2009. "The structure of dynamic correlations in multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 150(2), pages 182-192, June.
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Citations

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Cited by:
  1. Alessandro Fedele & Francesco Liucci & Andrea Mantovani, 2009. "Credit availability in the crisis: the European investment bank group," Working Papers 0913, University of Brescia, Department of Economics.
  2. Alessandra Del Boca & Michele Fratianni & Franco Spinelli & Carmine Trecroci, 2008. "The Phillips Curve and the Italian Lira, 1861-1998," Mo.Fi.R. Working Papers 8, Money and Finance Research group (Mo.Fi.R.) - Univ. Politecnica Marche - Dept. Economic and Social Sciences.
  3. 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, vol. 134(1), pages 224-237, November.
  4. Alessandro Fedele & Paolo Panteghini & Sergio Vergalli, 2010. "Optimal Investment and Financial Strategies under Tax Rate Uncertainty," CESifo Working Paper Series 3017, CESifo Group Munich.
  5. Alessandro Fedele & Raffaele Miniaci, 2009. "Do social enterprises finance their investments differently from for-profit firms? The case of social residential services in Italy," Working Papers 0911, University of Brescia, Department of Economics.
  6. Rosella Levaggi & Francesco Menoncin, 2009. "Decentralized provision of merit and impure public goods," Working Papers 0909, University of Brescia, Department of Economics.
  7. BISIN, Alberto & GEANAKOPOLS, John & GOTTARDI, Piero & MINELLI, Enrico & POLEMARCHAKIS, Herakles, 2011. "Markets and Contracts," Open Access publications from European University Institute urn:hdl:1814/19838, European University Institute.
  8. Martin Meier & Enrico Minelli & Herakles Polemarchakis, 2009. "Competitive Markets with Private Information on Both Sides," Working Papers 0917, University of Brescia, Department of Economics.
  9. Monica Billio & Roberto Casarin, 2010. "Bayesian Estimation of Stochastic-Transition Markov-Switching Models for Business Cycle Analysis," Working Papers 1002, University of Brescia, Department of Economics.
  10. Francesco Menoncin & Paolo Panteghini, 2009. "Retrospective Capital Gains Taxation in the Real World," CESifo Working Paper Series 2674, CESifo Group Munich.

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