Linear and Nonlinear Time Series Model Selection for Stationary Data Structure: Application to Monthly Rainfall Data in Nigeria

Abstract

Many available techniques for time series modeling assume linear relationship among variables. However in some situations, variations in data do not exhibit simple regularities and are difficult to model accurately. Linear relationship and their arrangements for describing the behaviour of such data are often found to be inadequate. Since many real life data are nonlinear, there is need to investigate which models can best captured data that are linear as well as those that are nonlinear. This paper examined the performances of the following nonlinear time series model: Self Exiting Threshold Autoregressive (SETAR), Smooth Transition Autoregressive (STAR) and Logistic Smooth Transition Autoregressive (LSTAR) models in fitting general classes of linear and nonlinear autoregressive cases at different sample sizes. The relative performances of the models were examined, within the context of stationarity, and compared with linear Autoregressive (AR). The LSTAR was the best as sample size was increased for different nonlinear autoregressive functions except in polynomial function where SETAR models out-performed others. The performances of the four fitted models increased when sample size was increased. Finally, we demonstrated the application of the models stated earlier on data of monthly rainfall in Nigeria between 1973-2013. SETAR model fitted best to the Rainfall data and LSTAR was the best when the data was transformed to nonlinear.