Compare the Performances and Identification of Optimal Lag Order on Selected Linear and Non-Linear Time Series Models of Different Orders

Abstract

This study sets out to evaluate and compare the performance of Autoregressive (AR) 
models against modified versions of several smooth transition autoregressive 
models, including Inverse Smooth Transition Autoregressive (ISTAR), Exponential 
Smooth Transition Autoregressive (ESTAR) and Trigonometric Smooth Transition 
Autoregressive (TSTAR) models. Specifically, we examine how these models perform 
across varying sample sizes and different orders. A comprehensive numerical 
simulation was conducted to assess the relative efficiency of both linear and 
nonlinear models, with sample sizes ranging from 20 to 250, for models of the first, 
second, and third orders. The evaluation of each model's performance is based on 
widely used statistical selection criteria, such as the Bayesian Information Criterion 
(BIC), Hannan-Quinn Information Criterion (HQC), and Akaike Information Criterion 
(AIC). For each order, the model with the lowest value for a given criterion is 
considered the most suitable. The findings indicate that, for second-order models, 
AR models consistently outperform their smooth transition counterparts, as 
evidenced by lower AIC and BIC values. However, for third-order models, the TSTAR 
model emerges as the most effective, outperforming other models based on HQC 
and AIC. These results highlight the strengths and weaknesses of both linear and 
nonlinear models at different complexity levels, providing useful insights into model 
selection for time series analysis.