Abstract
A test procedure based on continuous observation to detect a change in drift parameters of an ergodic diffusion process is proposed. The asymptotic behavior of a random field relating to an estimating equation under the null hypothesis is established using weak convergence theory in separable Hilbert spaces. This result is applied to a change point detection test.
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Acknowledgments
The author thanks to Professor Shuhei Mano for comments on proofs and Professor Yoichi Nishiyama for many suggestions. The author also thanks to the referees and the associate editor for their feedbacks which improved this paper.
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The large part of this paper is based on the thesis of the author at SOKENDAI (The Graduate University for Advanced Studies). The revision was done when the author was a member of Kurume University, Fukuoka. The author was a Research Fellow of Japan Society for the Promotion of Science and this work was partly supported by JSPS KAKENHI Grant Number 26-1487 (Grant-in-Aid for JSPS Fellows).
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Tsukuda, K. A change detection procedure for an ergodic diffusion process. Ann Inst Stat Math 69, 833–864 (2017). https://doi.org/10.1007/s10463-016-0564-y
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DOI: https://doi.org/10.1007/s10463-016-0564-y