The Empirical Likelihood for First-Order Random Coefficient Integer-Valued Autoregressive Processes

Abstract

This article studies the empirical likelihood method for the first-order random coefficient integer-valued autoregressive process. The limiting distribution of the log empirical likelihood ratio statistic is established. Confidence region for the parameter of interest and its coverage probabilities are given, and hypothesis testing is considered. The maximum empirical likelihood estimator for the parameter is derived and its asymptotic properties are established. The performances of the estimator are compared with the conditional least squares estimator via simulation.

Keywords:

• Asymptotic distribution
• Conditional least squares
• Hypothesis testing
• INAR model
• Maximum empirical likelihood

Mathematics Subject Classification:

• 62M10
• 62F10
• 62F03

Acknowledgments

We thank the referee for valuable suggestions which greatly improved the article. This work is supported by National Natural Science Foundation of China grants (No. 10971081, 10926156, 11001105), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20070183023, 20090061120037), Program for New Century Excellent Talents in University grant (NCET-08-237), Scientific Research Fund of Jilin University (No. 200810024, 200903278), Graduate Innovation Fund of Jilin University (No. 20101042) and 985 Project of Jilin University.