A Semiparametric Empirical Likelihood Estimation Method for Mixed Integer-Valued Autoregressive Model

This paper investigates a first-order mixed integer-valued autoregressive model based on the binomial thinning operator. The proposed MINAR(1) model allows the count process to evolve under heterogeneous autoregressive mechanisms and therefore provides greater flexibility for modeling count time series with structural heterogeneity. To estimate the unknown parameters, a maximum empirical likelihood estimation (MEL) procedure is developed using conditional moment restrictions. Compared with conventional likelihood-based methods, the proposed approach does not require a full specification of the innovation distribution and is therefore more robust to potential distributional misspecification. The consistency and asymptotic normality of the proposed MEL estimator are established under suitable regularity conditions. Simulation studies demonstrate that the MEL estimator performs satisfactorily in finite samples and exhibits competitive estimation accuracy compared with the maximum likelihood estimation (MLE). Finally, an application to monthly insurance claim counts illustrates the practical usefulness of the proposed method.