Bayesian estimation of switching ARMA models. (English) Zbl 1070.62515
Summary: Switching ARMA processes have recently appeared as an efficient modelling to nonlinear time-series models, because they can represent multiple or heterogeneous dynamics through simple components. The levels of dependence between the observations are double: at a first level, the parameters of the model are selected by a Markovian procedure. At a second level, the next observation is generated according to a standard time-series model. When the model involves a moving average structure, the complexity of the resulting likelihood function is such that simulation techniques, like those proposed by N. Shephard [Biometrika 81, No. 1, 115–131 (1994; Zbl 0796.62079)] and M. Billio and A. Monfort [J. Stat. Plann. Inference 68, No. 1, 65–103 (1998; Zbl 0944.62085)], are necessary to derive an inference on the parameters of the model. We propose in this paper a Bayesian approach with a non-informative prior distribution developed in K. L. Mengersen and C. P. Robert [Bayesian Statistics 5. Oxford University Press, Oxford, pp. 255–276 (1996)] and C. P. Robert and M. Titterington [Stat. Comput. 8, No. 2, 145–158 (1998)] in the setup of mixtures of distributions and hidden Markov models, respectively. The computation of the Bayes estimates relies on MCMC techniques which iteratively simulate missing states, innovations and parameters until convergence. The performances of the method are illustrated on several simulated examples. This work also extends the papers by S. Chib and E. Greenberg [J. Econom. 64, No. 1–2, 183–206 (1994; Zbl 0807.62065)] and S. Chib [J. Econom. 75, No. 1, 79–97 (1996; Zbl 0864.62010)] which deal with ARMA and hidden Markov models, respectively.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62F15 | Bayesian inference |
| 62M05 | Markov processes: estimation; hidden Markov models |
| 65C40 | Numerical analysis or methods applied to Markov chains |
Keywords:
Markov model; Moving average model; Hidden Markov chain; MCMC algorithm; ARMA model; Convergence control; Prior feedbackReferences:
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