Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 3, pp. 459-475

BAYESIAN INFERENCE FOR VECTOR ARMA MODELS WITH STABLE INNOVATIONS

By

ZUQIANG QIOU, Palisades Research Inc
and
NALINI RAVISHANKER, University of Connecticut, Storrs

SUMMARY. This article describes Bayesian inference for a multivariate time series model with infinite variance stable innovations. Specifically, the innovations are generated from a class of multivariate symmetric stable distributions while a vector autoregressive moving average (VARMA) process characterizes the stochastic evolution of the multiple time series. The Bayesian approach facilitates simultaneous estimation of the parameters characterizing the stable law, together with the parameters of the VARMA model. Our approach uses a Metropolis-Hastings algorithm to generate samples from the joint posterior distribution of all the parameters and is an extension to multivariate time series processes of Qiou and Ravishanker's (1997) approach for the univariate case. We illustrate our approach using simulated data.

AMS (1991) subject classification. 62A15, 62E25, 62F15, 62M10.

Key words and phrases. Infinite variance, metropolis- hastings algorithm, posterior distribution, VARMA models.

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