Locally Most Powerful Test for the Random Coefficient Autoregressive Model

In this article, we study the problem of testing the constancy of the coefficient in a class of stationary first-order random coefficient autoregressive (RCAR(1)) model. We construct a new test statistic based on the locally most powerful-type (LMP) test. Under the null hypothesis, we derive the limiting distribution of the proposed test statistic. In the simulation, we compare the power between LMP test and empirical likelihood (EL) test and find that the accuracy of using LMP is 6.7%, 28.8%, and 26.1% higher than that of EL test under normal, student’s t, and symmetric contamination errors, respectively. A real life data is given to illustrate the practical effectiveness of our test.