Statistical inference for generalized random coefficient autoregressive model

In this paper, we consider the application of the empirical likelihood method to the generalized random coefficient autoregressive (GRCA) model. The empirical log-likelihood ratio statistics are proposed and the nonparametric versions of the Wilk's theorem are obtained. Furthermore, when the order of the model is 1, we also derive a test statistic to test the stationary-ergodicity based on the conditional least-squares method. Numerical results from simulation studies suggest that the empirical likelihood method is more accurate than the normal approximation-based method of Hwang and Basawa (1998) [1]. Some simulation studies are also conducted to investigate the finite sample performances of the proposed test.