Comparative Study of Some Selected Linear and Non-Linear Time Series Models of Different Orders

Abstract

This study aims to evaluate and contrast the effectiveness of Autoregressive models with modified iterations of Inverse Smooth Transition Autoregressive (ISTAR), Exponential Smooth Transition Autoregressive (ESTAR), and Trigonometric Smooth Transition Autoregressive (TSTAR) models. We examine the impact of varying sample sizes on these models at different orders. A numerical simulation was done to assess the efficiency of linear and nonlinear models over sample sizes ranging from 20 to 250 for first, second, and third orders. The best-fit model at each order is determined using standard selection criteria, such as Mean Absolute Percentage Error (MAPE), Mean Square Error (MSE), and Akaike Information Criteria (AIC). The model that has the lowest value for the chosen criteria is considered the most optimal. The results suggest that AR models have superior performance for the second order, as determined by AIC and MAPE. On the other hand, TSTAR models exhibit better performance than other models for the third order, as indicated by MSE and AIC.