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

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  • Charles Bos
  • Neil Shephard

Abstract

In this paper we model the Gaussian errors in the standard Gaussian linear state space model as stochastic volatility processes. We show that conventional MCMC algorithms for this class of models are ineffective, but that the problem can be alleviated by reparameterizing the model. Instead of sampling the unobserved variance series directly, we sample in the space of the disturbances, which proves to lower correlation in the sampler and thus increases the quality of the Markov chain. Using our reparameterized MCMC sampler, it is possible to estimate an unobserved factor model for exchange rates between a group of n countries. The underlying n + 1 country-specific currency strength factors and the n + 1 currency volatility factors can be extracted using the new methodology. With the factors, a more detailed image of the events around the 1992 EMS crisis is obtained. We assess the fit of competitive models on the panels of exchange rates with an effective particle filter and find that indeed the factor model is strongly preferred by the data.

Suggested Citation

  • Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
  • Handle: RePEc:taf:emetrv:v:25:y:2006:i:2-3:p:219-244 DOI: 10.1080/07474930600713275
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    References listed on IDEAS

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    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, 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. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    4. Charles S. Bos & Ronald J. Mahieu & Herman K. Van Dijk, 2000. "Daily exchange rate behaviour and hedging of currency risk," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 671-696.
    5. 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.
    6. 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.
    7. 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, vol. 12(4), pages 413-417, October.
    8. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    9. repec:bla:restud:v:65:y:1998:i:3:p:361-93 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. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
    12. 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.
    13. Harvey, Andrew C & Koopman, Siem Jan, 1992. "Diagnostic Checking of Unobserved-Components Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 377-389, October.
    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.
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    Citations

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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, pages 1-30.
    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 Series Working Papers 644, University of Oxford, Department of Economics.
    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, pages 2911-2930.
    7. I. Sebastian Buhai & Miguel A. Portela & Coen N. Teulings & Aico van Vuuren, 2014. "Returns to Tenure or Seniority?," Econometrica, Econometric Society, vol. 82(2), pages 705-730, March.
    8. Neil Shephard, 2013. "Martingale unobserved component models," Economics Series Working Papers 644, University of Oxford, Department of Economics.
    9. Grassi Stefano & Proietti Tommaso, 2010. "Has the Volatility of U.S. Inflation Changed and How?," Journal of Time Series Econometrics, De Gruyter, pages 1-22.
    10. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    11. 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.
    12. 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, pages 4116-4125.

    More about this item

    Keywords

    Markov chain Monte Carlo; Particle filter; 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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