Change Point Testing for the Drift Parameters of a Periodic Mean Reversion Process

The problem of testing for a change in the parameters of a stochastic process has been an important issue in statistical inference for a long time. Initially investigated for i.i.d. data, change point analysis has more recently been extended to time series of dependent data. For a general review of change-point analysis, see e.g. the book by Csörgő and Horvath [4]. In the present paper, we investigate the problem of detecting changes in the drift parameters of a diffusion process. Diffusion processes are a popular and widely studied class of models with applications in economics, finance, physics and engineering. Statistical inference for diffusion processes has been investigated by many authors, see e.g. the monographs by Liptser and Shiryaev [17] and by Kutoyants [16]. However, change point analysis for diffusion processes has found little attention up to now. We mention the papers by Beibel [1], Lee, Nishiyama and Yoshida [11], Mihalache [12] and Negri and Nishiyama [13], where tests for the change points in the drift parameters of diffusions are discussed. However, all those papers deal with drift which stays constant in time before and after the eventual parameter change. In our paper, we focus on change-point analysis for a special class of diffusion processes, namely for so-called generalized Ornstein-Uhlenbeck processes. These processes are defined as solutions to the stochastic differential equation