Bayesian estimation of switching ARMA models

Switching ARMA processes have recently appeared as an efficient modelling t o nonlinear time-series models, because they can represent multiple or hete rogeneous dynamics through simple components. The levels of dependence betw een the observations are double: at a first level, the parameters of the mo del are selected by a Markovian procedure. At a second level, the next obse rvation is generated according to a standard time-series model. When the mo del involves a moving average structure, the complexity of the resulting li kelihood function is such that simulation techniques, like those proposed b y Shephard (1994, Biometrika 81, 115-131) and Billio and Monfort (1998, Jou rnal of Statistical Planning and Inference 68, 65-103), are necessary to de rive an inference on the parameters of the model. We propose in this paper a Bayesian approach with a non-informative prior distribution developed in Mengersen and Robert (1996, Bayesian Statistics 5. Oxford University Press, Oxford, pp. 255-276) and Robert and Titterington (1998, Statistics and Com puting 8(2), 145-158) 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 a nd parameters until convergence. The performances of the method are illustr ated on several simulated examples. This work also extends the papers by Ch ib and Greenberg (1994, Journal of Econometrics 64, 183-206) and Chib (1996 , Journal of Econometrics 75(1), 79-97) which deal with ARMA and hidden Mar kov models, respectively. (C) 1999 Elsevier Science S.A. All rights reserve d.