On threshold moving‐average models

In this paper the class of discrete self‐exciting threshold moving‐average (SETMA) models is studied in some detail. In particular, we consider various problems associated with the identification, estimation and testing of these models. A simple method for distinguishing between low order moving average (MA) and low order SETMA models is presented. Some simulation results illustrate the performance of the proposed method. We also derive a Lagrange multiplier (LM) test statistic for testing a linear MA model against a SETMA model. The small sample performance of the LM test is evaluated in a Monte Carlo study. A real example is used to illustrate the results.