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Skew Generalized Normal Innovations for the AR(p) Process Endorsing Asymmetry
Symmetry ( IF 2.940 ) Pub Date : 2020-07-29 , DOI: 10.3390/sym12081253
Ané Neethling , Johan Ferreira , Andriëtte Bekker , Mehrdad Naderi

The assumption of symmetry is often incorrect in real-life statistical modeling due to asymmetric behavior in the data. This implies a departure from the well-known assumption of normality defined for innovations in time series processes. In this paper, the autoregressive (AR) process of order p (i.e., the AR(p) process) is of particular interest using the skew generalized normal (SGN) distribution for the innovations, referred to hereafter as the ARSGN(p) process, to accommodate asymmetric behavior. This behavior presents itself by investigating some properties of the SGN distribution, which is a fundamental element for AR modeling of real data that exhibits non-normal behavior. Simulation studies illustrate the asymmetry and statistical properties of the conditional maximum likelihood (ML) parameters for the ARSGN(p) model. It is concluded that the ARSGN(p) model accounts well for time series processes exhibiting asymmetry, kurtosis, and heavy tails. Real time series datasets are analyzed, and the results of the ARSGN(p) model are compared to previously proposed models. The findings here state the effectiveness and viability of relaxing the normal assumption and the value added for considering the candidacy of the SGN for AR time series processes.

中文翻译:

支持不对称性的 AR(p) 过程的偏斜广义正态创新

由于数据中的不对称行为,对称性假设在现实生活中的统计建模中通常是不正确的。这意味着背离了为时间序列过程中的创新定义的众所周知的正态性假设。在本文中,使用偏斜广义正态 (SGN) 分布进行创新的 p 阶自回归 (AR) 过程(即 AR(p) 过程)特别令人感兴趣,以下称为 ARSGN(p) 过程,以适应不对称行为。这种行为是通过研究 SGN 分布的一些属性来呈现的,这是对表现出非正态行为的真实数据进行 AR 建模的基本要素。模拟研究说明了 ARSGN(p) 模型的条件最大似然 (ML) 参数的不对称性和统计特性。得出的结论是,ARSGN(p) 模型很好地解释了表现出不对称、峰态和重尾的时间序列过程。分析实时序列数据集,并将 ARSGN(p) 模型的结果与先前提出的模型进行比较。此处的发现说明了放宽正常假设的有效性和可行性,以及考虑 SGN 对 AR 时间序列过程的候选资格的附加值。
更新日期:2020-07-29
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