Test for Parameter Change in Linear Processes Based on Whittle's Estimator

Abstract

In this article, we develop a cusum test for testing for parameter changes in linear processes based on Whittle's estimator. It is shown that under regularity conditions, the test statistic converges to the sup of a Brownian bridge. The result is particularly useful in handling the change point test in stationary ARMA processes. A simulation result is provided for illustration.

Keywords:

• Brownian bridge
• Cusum test
• Linear process
• Test for parameter change
• Weak convergence
• Whittle's estimator

Mathematics Subject Classification:

• Primary 62M10
• Secondary 62G20

Acknowledgments

We are grateful to an Associate Editor and a referee for their valuable comments that helped improve the quality of this article. We wish to acknowledge that this research was supported (in part) by KOSEF through the Statistical Research Center for Complex Systems at Seoul National University.