Symmetrical and asymmetrical mixture autoregressive processes.(English)Zbl 1445.62233

Summary: In this paper, we study the finite mixtures of autoregressive processes assuming that the distribution of innovations (errors) belongs to the class of scale mixture of skew-normal (SMSN) distributions. The SMSN distributions allow a simultaneous modeling of the existence of outliers, heavy tails and asymmetries in the distribution of innovations. Therefore, a statistical methodology based on the SMSN family allows us to use a robust modeling on some non-linear time series with great flexibility, to accommodate skewness, heavy tails and heterogeneity simultaneously. The existence of convenient hierarchical representations of the SMSN distributions facilitates also the implementation of an ECME-type of algorithm to perform the likelihood inference in the considered model. Simulation studies and the application to a real data set are finally presented to illustrate the usefulness of the proposed model.

MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62P20 Applications of statistics to economics

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