Empirical Likelihood for an Autoregressive Model with Explanatory Variables

Abstract

In this article, we use the empirical likelihood method to construct the confidence region for parameters in autoregressive model with martingale difference error. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. The simulation results suggest that the empirical likelihood method outperforms the normal approximation based method in terms of coverage probability.

Keywords:

• Asymptotic normality
• Autoregressive model
• Confidence region
• Empirical likelihood
• Least squares estimation

Mathematics Subject Classification:

• Primary 62M10
• Secondary 91B62

Acknowledgments

This work is supported by National Natural Science Foundation of China (No. 10971081, 11001105, 11071126, 10926156, J0730101), Specialized Research Fund for the Doctoral Program of Higher Education (No. 20070183023), Program for New Century Excellent Talents in University (NCET-08-237), Scientific Research Fund of Jilin University (No. 200810024, 200903278), and 985 project of Jilin University.