Premium
Estimation for change point of discretely observed ergodic diffusion processes
Author(s) -
Tonaki Yozo,
Kaino Yusuke,
Uchida Masayuki
Publication year - 2023
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12567
Subject(s) - ergodic theory , diffusion , estimator , mathematics , diffusion process , statistical physics , convergence (economics) , estimation theory , point (geometry) , change detection , statistics , mathematical analysis , computer science , physics , geometry , innovation diffusion , thermodynamics , artificial intelligence , economics , economic growth , knowledge management
We treat the change point problem in ergodic diffusion processes from discrete observations. Tonaki et al. (2021a) proposed adaptive tests for detecting changes in the diffusion and drift parameters in ergodic diffusion process models. When any change in the diffusion or drift parameter is detected by this or any other method, the next question to consider is where the change point is located. Therefore, we propose the method to estimate the change point of the parameter for two cases: the case where there is a change in the diffusion parameter, and the case where there is no change in the diffusion parameter but a change in the drift parameter. Furthermore, we present rates of convergence and distributional results of the change point estimators. Some examples and simulation results are also given.