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

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Author Info

  • Charles S. Bos

    () (Tinbergen Institute and Vrije Universiteit Amsterdam,The Netherlands)

  • Neil Shephard

    () (Nuffield College, Oxford University, UK)

Abstract

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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Bibliographic Info

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

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Web page: http://www.nuff.ox.ac.uk/economics/

Related research

Keywords: Markov chain Monte Carlo; particle filter; cubic spline; state space form; stochastic volatility.;

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References

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  1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  2. 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.
  3. Charles S. Bos, 2002. "A Comparison of Marginal Likelihood Computation Methods," Tinbergen Institute Discussion Papers 02-084/4, Tinbergen Institute.
  4. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
  5. 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.
  6. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  7. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  8. Bos, C.S. & Mahieu, R.J. & Dijk, H.K. van, 2000. "Daily exchange rate behaviour and hedging of currency risk," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3131740, Tilburg University.
  9. Uhlig, H.F.H.V.S., 1996. "Bayesian Vector Autoregressions with Stochastic Volatility," Discussion Paper 1996-09, Tilburg University, Center for Economic Research.
  10. 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.
  11. Harvey, A. C. & Ruiz, Esther & Sentana, E., 1992. "Unobserved Component Time Series Models with ARCH Disturbances," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4702, Universidad Carlos III de Madrid.
  12. 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.
  13. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
  14. Harvey, A.C. & Koopman, S.J.M., 1999. "Signal Extraction and the Formulation of Unobserved Components Models," Discussion Paper 1999-44, Tilburg University, Center for Economic Research.
  15. 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.
  16. 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.
  17. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1995. "Multivariate Stochastic Variance Models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/4783, Universidad Carlos III de Madrid.
  18. 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.
  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.
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Citations

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Cited by:
  1. Chris M Strickland & Gael Martin & Catherine S Forbes, 2006. "Parameterisation and Efficient MCMC Estimation of Non-Gaussian State Space Models," Monash Econometrics and Business Statistics Working Papers 22/06, Monash University, Department of Econometrics and Business Statistics.
  2. Neil Shephard, 2013. "Martingale unobserved component models," Economics Papers 2013-W01, Economics Group, Nuffield College, University of Oxford.
  3. Michel Beine & Charles S. Bos & Sebastian Laurent, 2005. "The Impact of Central Bank FX Interventions on Currency Components," Tinbergen Institute Discussion Papers 05-103/4, Tinbergen Institute.
  4. Charles S. Bos, 2008. "Model-based Estimation of High Frequency Jump Diffusions with Microstructure Noise and Stochastic Volatility," Tinbergen Institute Discussion Papers 08-011/4, Tinbergen Institute.
  5. Carmen Broto & Esther Ruiz, 2008. "Testing for conditional heteroscedasticity in the components of inflation," Banco de España Working Papers 0812, Banco de España.
  6. Creal, D., 2009. "A survey of sequential Monte Carlo methods for economics and finance," Serie Research Memoranda 0018, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  7. Strickland, Chris M. & Turner, Ian. W. & Denham, Robert & Mengersen, Kerrie L., 2009. "Efficient Bayesian estimation of multivariate state space models," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4116-4125, October.
  8. Neil Shephard, 2013. "Martingale unobserved component models," Economics Series Working Papers 644, University of Oxford, Department of Economics.

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