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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 () (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)
Neil Shephard () (Nuffield College, University of Oxford)

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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 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.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 04-015/4.

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Date of creation: 27 Jan 2004
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Handle: RePEc:dgr:uvatin:20040015

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

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Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
F31 - International Economics - - International Finance - - - Foreign Exchange

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. C.S. Bos & R.J. Mahieu & H.K. Van Dijk, 2000. "Daily exchange rate behaviour and hedging of currency risk," Econometric Institute Report 201, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
    Other versions:
  3. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. Charles S. Bos, 2002. "A Comparison of Marginal Likelihood Computation Methods," Tinbergen Institute Discussion Papers 02-084/4, Tinbergen Institute. [Downloadable!]
  6. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  7. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
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  8. 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. [Downloadable!] (restricted)
  9. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  10. 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. [Downloadable!] (restricted)
  11. 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.
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  12. 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. [Downloadable!] (restricted)
  13. 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.
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  14. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 361-93, July. [Downloadable!] (restricted)
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  15. 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. [Downloadable!]
  16. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Oxford University Press for Biometrika Trust, vol. 89(3), pages 603-616, August.
  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. [Downloadable!] (restricted)
  18. 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.
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  19. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 247-64, April. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
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