Rank tests for testing the randomness of autoregressive coefficients

Abstract

We propose a class of rank tests for testing the randomness of the regression coefficients in a random coefficient autoregressive model. Asymptotic distributions of these tests are obtained via weak convergence results of a randomly weighted residual empirical process proved by Koul and Ossiander (1993). The proposed rank tests are found to be asymptotically distribution free under H 0. The asymptotic relative efficiency (ARE) (in the Pitman sense) of a rank test with respect to the score test for a Gaussian model is obtained.