Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series B, Pt. 3, pp. 353--371

BAYESIAN ANALYSIS OF THRESHOLD AUTOREGRESSIVE MOVING AVERAGE MODELS

By

THELMA SÁFADI, Federal University of Lavras, Brazil

and

PEDRO A. MORRETIN, University of São Paulo, Brazil

SUMMARY. In this paper we consider a Bayesian analysis for threshold autoregressive moving average models. Two different methods are used for the special case of two regimes. In the first we consider a hierarchical prior and obtain posterior distributions in closed form. In the second, a rearranged procedure due Tsay (1989) is used, in conjunction with the Gibbs sampler and Metropolis-Hastings algorithm. Applications are given for a simulated series and for the sunspot data.

AMS (1991) subject classification. 62F15, 62M10.

Key words and phrases. ARMA models, Bayesian analysis, Gibbs sampler, Metropolis-Hastings algorithm, predictive distribution, rearranged autoregression, TARMA model, threshold.

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