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This paper studies the empirical likelihood method for a multivariate first-order random coefficient autoregressive (RCAR(1)) model. Based on the modified least square score equation, empirical likelihood method is used to test the randomness of coefficients and estimate the unknown parameters. First, the limiting distribution of the log empirical likelihood ratio statistic is established. Second, the maximum empirical likelihood estimator is derived and its asymptotic properties are established. Finally, the performances of the estimator are compared with the modified least square estimator via simulation. Furthermore, simulation result shows that the test has the correct size and very good power for all cases considered.

Estimation and testing of multivariate random coefficient autoregressive model based on empirical likelihood