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Skew Generalized Normal Innovations for the AR(p) Process Endorsing Asymmetry

Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria 0028, South Africa
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Symmetry 2020, 12(8), 1253; https://doi.org/10.3390/sym12081253
Received: 7 July 2020 / Revised: 23 July 2020 / Accepted: 26 July 2020 / Published: 29 July 2020
(This article belongs to the Section Mathematics and Symmetry/Asymmetry)
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. View Full-Text
Keywords: conditional maximum likelihood estimator; skew-t; generalized normal; heavy tails; skewness conditional maximum likelihood estimator; skew-t; generalized normal; heavy tails; skewness
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MDPI and ACS Style

Neethling, A.; Ferreira, J.; Bekker, A.; Naderi, M. Skew Generalized Normal Innovations for the AR(p) Process Endorsing Asymmetry. Symmetry 2020, 12, 1253. https://doi.org/10.3390/sym12081253

AMA Style

Neethling A, Ferreira J, Bekker A, Naderi M. Skew Generalized Normal Innovations for the AR(p) Process Endorsing Asymmetry. Symmetry. 2020; 12(8):1253. https://doi.org/10.3390/sym12081253

Chicago/Turabian Style

Neethling, Ané, Johan Ferreira, Andriëtte Bekker, and Mehrdad Naderi. 2020. "Skew Generalized Normal Innovations for the AR(p) Process Endorsing Asymmetry" Symmetry 12, no. 8: 1253. https://doi.org/10.3390/sym12081253

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