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.
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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.