Identification of threshold autoregressive moving average models

Abstract

Due to the lack of a suitablemodeling procedure and the difficulty to identify the threshold variable and estimate the threshold values, the threshold autoregressive moving average (TARMA) model with multi-regime has not attracted much attention in application. Therefore, the chief goal of our paper is to propose a simple and yet widely applicable modeling procedure for multi-regime TARMA models. Under no threshold case, we utilize extended least squares estimate (ELSE) and linear arranged regression to obtain a test statistic F, which is proved to follow an approximate F distribution. And then, based on the statistic F, we employ some scatter plots to identify the number and locations of the potential thresholds. Finally, the procedures are considered to build a TARMA model by these statistics and the Akaike information criterion (AIC). Simulation experiments and the application to a real data example demonstrate that both the power of the test statistic and the model-building can work very well in the case of TARMA models.