{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,2]],"date-time":"2026-08-02T23:25:05Z","timestamp":1785713105226,"version":"3.56.0"},"reference-count":33,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,2]],"date-time":"2020-06-02T00:00:00Z","timestamp":1591056000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a Bayesian analysis of finite mixture autoregressive (MAR) models based on the assumption of scale mixtures of skew-normal (SMSN) innovations (called SMSN\u2013MAR) is considered. This model is not simultaneously sensitive to outliers, as the celebrated SMSN distributions, because the proposed MAR model covers the lightly\/heavily-tailed symmetric and asymmetric innovations. This model allows us to have robust inferences on some non-linear time series with skewness and heavy tails. Classical inferences about the mixture models have some problematic issues that can be solved using Bayesian approaches. The stochastic representation of the SMSN family allows us to develop a Bayesian analysis considering the informative prior distributions in the proposed model. Some simulations and real data are also presented to illustrate the usefulness of the proposed models.<\/jats:p>","DOI":"10.3390\/sym12060929","type":"journal-article","created":{"date-parts":[[2020,6,3]],"date-time":"2020-06-03T04:12:09Z","timestamp":1591157529000},"page":"929","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Bayesian Approach to Heavy-Tailed Finite Mixture Autoregressive Models"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4686-0930","authenticated-orcid":false,"given":"Mohammad Reza","family":"Mahmoudi","sequence":"first","affiliation":[{"name":"Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam"},{"name":"Department of Statistics, Faculty of Science, Fasa University, Fasa 74616-86131, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2774-2464","authenticated-orcid":false,"given":"Mohsen","family":"Maleki","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Isfahan, Isfahan 8174673441, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Art and Sciences, Cankaya University, Balgat, 06530 Ankara, Turkey"},{"name":"Institute of Space Sciences, 077125 Magurele-Bucharest, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vu-Thanh","family":"Nguyen","sequence":"additional","affiliation":[{"name":"University of Economics and Law, Ho Chi Minh City 700000, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0410-8839","authenticated-orcid":false,"given":"Kim-Hung","family":"Pho","sequence":"additional","affiliation":[{"name":"Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1006\/jmva.2000.1960","article-title":"A general class of multivariate skew-elliptical distributions","volume":"79","author":"Branco","year":"2001","journal-title":"J. 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