Abstract: We considered the application of the  empirical likelihood (EL) method to the bivariate first-order integer-valued autoregressive (BINAR(1)) process. We first established the empirical likelihood ratio (ELR) statistics, discussed and found its limit distribution by using asymptotic normality of the conditional least squares (CLS) estimation of the process, thus constructed the confidence regions of the parameter and solved the problem of hypothesis test of the parameters. Then, the coverage probability of the confidence region of the parameters computed by EL methods and normal approximation (NA) methods was compared through numerical simulation.

Key words: BINAR(1) process, EL methods, ELR statistics, score function