Abstract:
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.
