Ratio test to detect change in the variance of linear process

Abstract

An adaptation of the method of Horváth et al. [Ratio tests for change point detection, Inst. Math. Stat. 1 (2008), pp. 293–304] is proposed to detect change in the variance of a linear process. In comparison with the existing tests, the new one does not require the estimation of the long-run variance. The test is robust against misspecification. Its asymptotic property is investigated under the no change null hypothesis. A Monte Carlo study shows that our test has reasonably good size and power properties in moderate samples. We also discuss how to estimate the change point which has not been discussed by the existing literatures. The consistency and rate of convergence for the change point estimator are also established. We demonstrate the applicability of our method to estimate the time of change of the variance of an ARMA(1,1) process. The effectiveness of the method is examined by analysing a real example.

Keywords:

• ratio test
• linear processes
• variance change point
• consistent test
• rate of convergence

AMS Subject Classification :

• 62F03
• 62F05

Acknowledgements

The authors gratefully acknowledge Professor Horváth since the research was completed after we have read Horváth et al. 11. Thanks also go to two referees for their helpful comments and insightful suggestions. This work was supported by the National Natural Science Foundation of China (grant no. 60375003), Aeronautics and Astronautics Basal Science Foundation of China (no. 03I53059) and the Science and Technology Innovation Foundation of Northwestern Polytechnical University (no. 2007KJ01033).