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

  • Charles Bos
  • Neil Shephard

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.

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Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 25 (2006)
Issue (Month): 2-3 ()
Pages: 219-244

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Handle: RePEc:taf:emetrv:v:25:y:2006:i:2-3:p:219-244
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  1. 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.
  2. 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.
  3. Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998. "Statistical algorithms for models in state space using SsfPack 2.2," Economics Series Working Papers 1998-W06, University of Oxford, Department of Economics.
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  5. 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, 77 Bastwick Street, London EC1V 3PZ..
  6. 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.
  7. 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.
  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. Michael K Pitt & Neil Shephard, . "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
  10. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  11. 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.
  12. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
  13. Shephard, Neil, 1994. "Local scale models : State space alternative to integrated GARCH processes," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 181-202.
  14. Neil Shephard & Siddhartha Chib, 1999. "Analysis of High Dimensional Multivariate Stochastic Volatility Models," Economics Series Working Papers 1999-W18, University of Oxford, Department of Economics.
  15. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  16. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  17. 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.
  18. 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.
  19. 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.
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