Change detection in the Cox–Ingersoll–Ross model
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Gyula Pap
Abstract
We propose an offline change detection method for the famous Cox–Ingersoll–Ross model based on a continuous sample. We develop one- and two-sided testing procedures for both drift parameters of the process. The test process is based on estimators that are motivated by the discrete time least-squares estimators, and its asymptotic distribution under the no-change hypothesis is that of a Brownian bridge. We prove the asymptotic weak consistence of the test, and derive the asymptotic properties of the change-point estimator under the alternative hypothesis of change at one point in time.
Funding source: European Social Fund
Award Identifier / Grant number: TÁMOP 4.2.4. A/2-11-1-2012-0001
Funding statement: This research was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP 4.2.4. A/2-11-1-2012-0001 “National Excellence Program”.
Acknowledgements
The authors are grateful to Professor Péter Major at the University of Szeged for supplying the basic idea of the proof of Lemma 7.8. We express our gratitude to the anonymous reviewers, whose comments have been most helpful in improving the readability of the paper.
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