Skew Generalized Normal Innovations for the AR(p) Process Endorsing Asymmetry
Skew Generalized Normal Innovations for the AR(p) Process Endorsing Asymmetry
复制标题
AR(p) 过程的偏斜广义正态创新支持不对称性
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Mehrdad Naderi
中科院分区：
文献类型：
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作者：
A. Neethling;J. Ferreira;A. Bekker;Mehrdad Naderi
由于数据的不对称行为，在实际统计建模中，对称性的假设常常是不正确的。这意味着偏离了众所周知的为时间序列过程中的创新定义的正态性假设。在本文中，p阶的自回归（AR）过程（即AR(p)过程）是特别有趣的，使用偏斜广义正态（SGN）分布进行创新，以下称为ARSGN(p)过程，以适应不对称行为。这种行为通过研究SGN分布的一些属性来表现出来，SGN分布是对显示非正态行为的真实数据进行AR建模的基本元素。仿真研究说明了ARSGN(p)模型的条件最大似然（ML）参数的不对称性和统计特性。结论是，ARSGN(p)模型很好地解释了表现出不对称、峰度和重尾的时间序列过程。对实时序列数据集进行了分析，并将ARSGN(p)模型的结果与先前提出的模型进行了比较。这里的研究结果说明了放松正常假设的有效性和可行性，以及考虑SGN是否适合AR时间序列过程的附加价值。
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.