Stochastic model specification search for Gaussian and partial non-Gaussian state space models
Model specification for state space models is a difficult task as one has to decide which components to include in the model and to specify whether these components are fixed or time-varying. To this aim a new model space MCMC method is developed in this paper. It is based on extending the Bayesian variable selection approach which is usually applied to variable selection in regression models to state space models. For non-Gaussian state space models stochastic model search MCMC makes use of auxiliary mixture sampling. We focus on structural time series models including seasonal components, trend or intervention. The method is applied to various well-known time series.
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- J. Durbin & S. J. Koopman, 2000.
"Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives,"
Journal of the Royal Statistical Society Series B,
Royal Statistical Society, vol. 62(1), pages 3-56.
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- Carmen Fernandez & Eduardo Ley & Mark F.J. Steel, 1998. "Benchmark Priors for Bayesian Model Averaging," Econometrics 9804001, EconWPA, revised 08 Oct 2001.
- Carmen Fernandez & Eduardo Ley & Mark F J Steel, 1998. "Benchmark priors for Bayesian model averaging," ESE Discussion Papers 66, Edinburgh School of Economics, University of Edinburgh.
- Fruhwirth-Schnatter, Sylvia & Fruhwirth, Rudolf, 2007. "Auxiliary mixture sampling with applications to logistic models," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3509-3528, April.
- Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
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- Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2008. "Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4608-4624, June.
- Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
- Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
- Tom Doan, "undated". "SEASONALDLM: RATS procedure to create the matrices for the seasonal component of a DLM," Statistical Software Components RTS00251, Boston College Department of Economics.
- Claudia Czado & Peter Song, 2008. "State space mixed models for longitudinal observations with binary and binomial responses," Statistical Papers, Springer, vol. 49(4), pages 691-714, October.
- Sylvia FrüHwirth-Schnatter & Helga Wagner, 2006. "Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling," Biometrika, Biometrika Trust, vol. 93(4), pages 827-841, December.
- Shively, Thomas S. & Kohn, Robert, 1997. "A Bayesian approach to model selection in stochastic coefficient regression models and structural time series models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 39-52.
- Sylvia Frühwirth-Schnatter, 2001. "Fully Bayesian Analysis of Switching Gaussian State Space Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 31-49, March.
- Smith M. & Kohn R., 2002. "Parsimonious Covariance Matrix Estimation for Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1141-1153, December. Full references (including those not matched with items on IDEAS)
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