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

Author

Listed:
  • Charles S. Bos

    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Neil Shephard

    (Nuffield College, University of Oxford)

Abstract

This discussion paper led to a publication in 'Econometric Reviews' , 2006, 25(2-3), 219-244. 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 algorithms 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 model. 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," Tinbergen Institute Discussion Papers 04-015/4, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20040015
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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. 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.
    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, 1999. "Analytic Convergence Rates and Parameterization Issues for the Gibbs Sampler Applied to State Space Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(1), pages 63-85, January.
    5. Aguilar, Omar & West, Mike, 2000. "Bayesian Dynamic Factor Models and Portfolio Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 338-357, July.
    6. 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.
    7. 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.
    8. Neil Shephard & Michael K Pitt, 1995. "Likelihood analysis of non-Gaussian parameter driven models," Economics Papers 15 & 108., Economics Group, Nuffield College, University of Oxford.
    9. 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.
    10. Martin D. D. Evans & Richard K. Lyons, 2017. "How is Macro News Transmitted to Exchange Rates?," World Scientific Book Chapters, in: Studies in Foreign Exchange Economics, chapter 14, pages 547-596, World Scientific Publishing Co. Pte. Ltd..
    11. Beine, Michel & Laurent, Sébastien & Palm, Franz C., 2009. "Central bank FOREX interventions assessed using realized moments," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(1), pages 112-127, February.
    12. 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.
    13. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    14. W. R. Gilks & N. G. Best & K. K. C. Tan, 1995. "Adaptive Rejection Metropolis Sampling Within Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 455-472, December.
    15. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    16. 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.
    17. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
    18. 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., vol. 15(6), pages 671-696.
    19. 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.
    20. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    21. 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.
    22. 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.
    23. Harvey,Andrew & Koopman,Siem Jan & Shephard,Neil (ed.), 2004. "State Space and Unobserved Component Models," Cambridge Books, Cambridge University Press, number 9780521835954, October.
    24. 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. 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.
    3. Michel Beine & Charles S. Bos & Sébastien Laurent, 2007. "The Impact of Central Bank FX Interventions on Currency Components," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 154-183.
    4. repec:jss:jstsof:41:i13 is not listed on IDEAS
    5. 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.
    6. Neil Shephard, 2013. "Martingale unobserved component models," Economics Series Working Papers 644, University of Oxford, Department of Economics.
    7. 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.
    8. Huang Yu-Fan, 2021. "An effcient exact Bayesian method For state space models with stochastic volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(2), pages 1-10, April.
    9. Charles S. Bos, 2011. "Relating Stochastic Volatility Estimation Methods," Tinbergen Institute Discussion Papers 11-049/4, Tinbergen Institute.
    10. Drew Creal, 2012. "A Survey of Sequential Monte Carlo Methods for Economics and Finance," Econometric Reviews, Taylor & Francis Journals, vol. 31(3), pages 245-296.
    11. 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.
    12. 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.
    13. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    14. 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.
    15. Kjartan Kloster Osmundsen & Tore Selland Kleppe & Roman Liesenfeld & Atle Oglend, 2021. "Estimating the Competitive Storage Model with Stochastic Trends in Commodity Prices," Econometrics, MDPI, vol. 9(4), pages 1-24, November.

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    More about this item

    Keywords

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

    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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