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Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form

  • Charles S. Bos

    ()

    (Tinbergen Institute and Vrije Universiteit Amsterdam,The Netherlands)

  • Neil Shephard

    ()

    (Nuffield College, Oxford University, UK)

In this paper we replace the Gaussian errors in the standard Gaussian, linear state space model with stochastic volatility processes. This is called a GSSF-SV model. We show that conventional MCMC algoritms for this type of model are ineffective, but that this problem can be removed by reparameterising the model. We illustrate our results on an example from financial economics and one from the nonparametric regression literature. We also develop an effective particle filter for this model which is useful to assess the fit of the model.

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File URL: http://www.nuff.ox.ac.uk/economics/papers/2004/W2/svssf_bosshep.pdf
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Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2004-W02.

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Length: 30 pages
Date of creation: 25 Feb 2004
Date of revision:
Handle: RePEc:nuf:econwp:042
Contact details of provider: Web page: http://www.nuff.ox.ac.uk/economics/

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  1. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
  2. Shephard, N. & Pitt, M.K., 1995. "Likelihood Analysis of Non-Gaussian Parameter-Driven Models," Economics Papers 108, Economics Group, Nuffield College, University of Oxford.
  3. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
  4. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
  5. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  6. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
  7. repec:dgr:uvatin:19990078 is not listed on IDEAS
  8. Koopman S.J. & Bos C.S., 2004. "State Space Models With a Common Stochastic Variance," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 346-357, July.
  9. repec:ner:tilbur:urn:nbn:nl:ui:12-3131740 is not listed on IDEAS
  10. Michael K Pitt & Neil Shephard, 1996. "Analytic convergence rates and parameterisation issues for the Gibbs sampler applied to state space models," Economics Papers 20 & 113, Economics Group, Nuffield College, University of Oxford.
  11. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
  12. Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 2000. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Econometric Society World Congress 2000 Contributed Papers 0504, Econometric Society.
  13. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
  14. 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.
  15. repec:dgr:uvatin:20020084 is not listed on IDEAS
  16. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  17. Rong Chen & Jun S. Liu, 2000. "Mixture Kalman filters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 493-508.
  18. Mahieu, Ronald & Schotman, Peter, 1994. "Neglected common factors in exchange rate volatility," Journal of Empirical Finance, Elsevier, vol. 1(3-4), pages 279-311, July.
  19. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
  20. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
  21. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  22. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
  23. repec:ner:tilbur:urn:nbn:nl:ui:12-3131741 is not listed on IDEAS
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