Time Series Based on Random Process of Unbounded Asymmetric Normal Distribution

Abstract

One of the generalizations of the normal distribution is the unlimited Skew normal distribution, which is more flexible than the classical normal distribution. In contrast to the normal distribution, the unlimited skewed normal distribution is an asymmetric distribution and includes various types of skewness. Therefore, it is used in fitting different types of real data. Therefore, we study the moving average autoregressive time series process based on the asymmetric normal coefficients of the unbounded Skew, or SUN-ARMA process for short. Providing a hierarchical representation of the unbounded Skew normal distribution facilitates the simulation of this distribution in practice. The parameters of the asymmetric SUN-ARMA process are estimated using the maximum likelihood method with the EM algorithm approach. The performance and accuracy of the maximum likelihood method in estimating the parameters of the SUN-ARMA process is investigated based on the simulated data under different sample sizes. Also, using two real data series, the efficiency of SUN-ARMA process is studied in comparison with the classical autoregressive process of moving average with normal coefficients, and the results confirm the superiority of SUN-ARMA process in fitting asymmetric real data.