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May 2020 Symmetrical and asymmetrical mixture autoregressive processes
Mohsen Maleki, Arezo Hajrajabi, Reinaldo B. Arellano-Valle
Braz. J. Probab. Stat. 34(2): 273-290 (May 2020). DOI: 10.1214/19-BJPS429


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.


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Mohsen Maleki. Arezo Hajrajabi. Reinaldo B. Arellano-Valle. "Symmetrical and asymmetrical mixture autoregressive processes." Braz. J. Probab. Stat. 34 (2) 273 - 290, May 2020.


Received: 1 March 2017; Accepted: 1 January 2019; Published: May 2020
First available in Project Euclid: 4 May 2020

zbMATH: 07232929
MathSciNet: MR4093259
Digital Object Identifier: 10.1214/19-BJPS429

Keywords: ECME algorithm , finite mixtures of autoregressive models , non-linear time series , scale mixtures of skew-normal distributions

Rights: Copyright © 2020 Brazilian Statistical Association


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Vol.34 • No. 2 • May 2020
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