Performance of Some Nonlinear Time Series Models on Non-Stationary Data

Abstract

Time series analyses are based on assumptions of linearity and stationarity, whereas many real life problems may not satisfy these assumptions. Thus, there is a need for further investigation of nonlinear time series models for cases that are non-stationary coupled with the features of nonlinearity. This study examines the Autoregressive (AR), Self Exiting Threshold Autoregressive (SETAR), Smooth Transition Autoregressive (STAR) and Logistic Smooth Transition Autoregressive (LSTAR) models. Mont-Carlo simulations are conducted using the R statistical package, to investigate the relative performances of these models at sample sizes of 50, 80, 100, 130, 150, 180, 200, 250, 300 and 400 based on the Mean Square Error (MSE), the Residual Variance (RV), the Akaike Information Criteria (AIC) and the Mean Absolute Percentage Error (MAPE). Thereafter, the models were fitted to data on exchange rate and their performances were evaluated. The study found that the LSTAR model outperformed others in all forms of the generated nonlinear autoregressive cases, except for the polynomial models (where SETAR is preferred to the others).