On Order Selection of Arima Models for Stationary Normal and Non-Normal Data Structures

1*Hamidu Aliyu Chamalwa, 2Imam Akeyede and 1Harun Rann Bakari

1Department of Mathematical Sciences, University of Maiduguri, PMB 1069, Borno State, Nigeria
2Department of Statistics, Federal University Lafia, PMB 146, Lafia Nigeria

*Corresponding Author: chamalwa@gmail.com doi.org/10.55639/607djpv


The study is aimed at identifying the orders of time series models in stationary and non-stationary non-normal data from different distributions; with a view to determining the best Autoregressive/ Moving Average orders from different time series, ARIMA models were considered for different underline distributions of data. The data is generated under normal uniform and exponential distribution using a second-order autoregressive model. Data were generated in two forms, these are, when stationarity is observed and when it is violated. Each case of data simulated is fitted to different models and the values of AIC, BIC, HQIC, and FPE are computed. The effect of different levels of parameters (0.3, 0.6, and -0.3, -0.6) at the sample size of 20, 40, 60, 80, 100, 120, 140, 160, 180, and 200 which we considered to represent moderate and large sample sizes respectively on the simulated data from the stationary normal and non-normal data. We concluded in general that the selections of the order for the models considered in this study are tied more to the underlying distribution of the series in relation to the Stationarity and non-Stationarity of the series as it will lead to the identification of the proper model. Since the selection are almost identical in the stationary and non-stationary from both normal and non-normal data structure but varies with the variation in the distribution of the series. And it was also observed that for the ARIMA models the order stocked to the principle of parsimony i.e. models with lower-order selected at most of the sample sizes considered. The need to develop a methodology for model selection that combines both objective and subjective techniques is strongly recommended.