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–MAR) 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.

中文翻译：

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重尾有限混合自回归模型的贝叶斯方法

在本文中，考虑了基于偏态正态 (SMSN) 创新（称为 SMSN-MAR）的尺度混合假设的有限混合自回归 (MAR) 模型的贝叶斯分析。该模型不像著名的 SMSN 分布那样同时对异常值敏感，因为所提出的 MAR 模型涵盖了轻/重尾对称和非对称创新。该模型允许我们对一些具有偏度和重尾的非线性时间序列进行稳健的推断。关于混合模型的经典推论有一些问题，可以使用贝叶斯方法解决。SMSN 族的随机表示允许我们考虑所提出模型中的信息先验分布来开发贝叶斯分析。