Cusum Test for Parameter Change Based on the Maximum Likelihood Estimator

Abstract

In this paper we consider the problem of testing for a parameter change based on the cusum test (cf. Lee, S.; Ha, J.; Na, O.; Na, S. The cusum test for parameter change in time series models. Scand. J. Statist. 2003, 30, 651–739) utilizing the maximum likelihood estimator. The issue is handled in iid random samples, and then special attention is paid to hidden Markov models. It is shown that the limiting distribution of the cusum test statistic is the sup of a standard Brownian bridge under regularity conditions. A simulation result is provided for illustration.

Key Words:

• Test for parameter change
• Cusum test based on the MLE
• Hidden Markov model
• Weak convergence
• Brownian bridge

Acknowledgments

We would like to thank the two referees for drawing our attention to the articles of Gombay and Horváth9 10. We wish to acknowledge that this work was supported by Korea Research Foundation Grant 2002-070-C00018.

Notes

Recommended by A. Gut