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

Author

Listed:
  • 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.

Suggested Citation

  • Charles S. Bos & Neil Shephard, 2004. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Economics Papers 2004-W02, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:042
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    References listed on IDEAS

    as
    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. 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.
    3. 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.
    4. 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.
    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. 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.
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    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. Beine, Michel & Bos, Charles S. & Coulombe, Serge, 2012. "Does the Canadian economy suffer from Dutch disease?," Resource and Energy Economics, Elsevier, vol. 34(4), pages 468-492.
    2. 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.
    3. Broto Carmen & Ruiz Esther, 2009. "Testing for Conditional Heteroscedasticity in the Components of Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-30, May.
    4. Michel Beine & Charles S. Bos & Sébastien Laurent, 2007. "The Impact of Central Bank FX Interventions on Currency Components," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 154-183.
    5. Neil Shephard, 2013. "Martingale unobserved component models," Economics Papers 2013-W01, Economics Group, Nuffield College, University of Oxford.
    6. Strickland, Chris M. & Martin, Gael M. & Forbes, Catherine S., 2008. "Parameterisation and efficient MCMC estimation of non-Gaussian state space models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2911-2930, February.
    7. 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.
    8. Grassi Stefano & Proietti Tommaso, 2010. "Has the Volatility of U.S. Inflation Changed and How?," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-22, September.
    9. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    10. 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.
    11. 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.

    More about this item

    Keywords

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

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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