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

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

Author Info

Charles S. Bos () (Tinbergen Institute and Vrije Universiteit Amsterdam,The Netherlands)
Neil Shephard () (Nuffield College, Oxford University, UK)

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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 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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Publisher 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/

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Article
Paper
- 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. [Downloadable!]

This paper has been announced in the following NEP Reports:

NEP-ALL-2004-02-29 (All new papers)
NEP-ECM-2004-03-03 (Econometrics)
NEP-ETS-2004-02-29 (Econometric Time Series)

References listed on IDEAS
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.:

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)
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:
- Bos, C.S. & Mahieu, R.J. & van Dijk, H.K., 1999. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Papers 9936/a, Erasmus University of Rotterdam - Econometric Institute.
- Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 1999. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Tinbergen Institute Discussion Papers 99-078/4, Tinbergen Institute. [Downloadable!]
- Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 2001. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Tinbergen Institute Discussion Papers 01-017/4, Tinbergen Institute. [Downloadable!]
- C.S. Bos & R.J. Mahieu & H.K. van Dijk, 1999. "Daily exchange rate behaviour and hedging of currency risk," Econometric Institute Report 164, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
- Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 2000. "Daily Exchange Rate Behaviour and Hedging of Currency Risk," Econometric Society World Congress 2000 Contributed Papers 0504, Econometric Society. [Downloadable!]
- 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. [Downloadable!]
Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
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Other versions:
- Ronald Mahieu & Peter Schotman, 1994. "Neglected Common Factors in Exchange Rate Volatility," CEPR Financial Markets Paper 0041, European Science Foundation Network in Financial Markets, c/o C.E.P.R, 53--56 Great Sutton Street, London EC1V 0DG.
Charles S. Bos, 2002. "A Comparison of Marginal Likelihood Computation Methods," Tinbergen Institute Discussion Papers 02-084/4, Tinbergen Institute. [Downloadable!]
Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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Other versions:
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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)
Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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)
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.
Other versions:
- Koopman, S.J. & Shephard, N. & Doornik, J.A., 1998. "Statistical algorithms for models in state space using ssfpack 2.2," Discussion Paper 141, Tilburg University, Center for Economic Research. [Downloadable!]
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)
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.
Other versions:
- Harvey, A. & Koopman, S.J., 1999. "Signal extraction and the formulation of unobserved components models," Discussion Paper 44, Tilburg University, Center for Economic Research. [Downloadable!]
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)
Other versions:
- Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
- Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford. [Downloadable!]
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA. [Downloadable!]
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!]
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.
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)
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.
Other versions:
- 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.
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)

Full references

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.)

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!]
Other versions:
- Michel Beine & Charles S. Bos & Sébastien Laurent, 2007. "The Impact of Central Bank FX Interventions on Currency Components," Journal of Financial Econometrics, Oxford University Press, vol. 5(1), pages 154-183. [Downloadable!] (restricted)

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