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Change point testing for the drift parameters of a periodic mean reversion process

Abstract

In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein-Uhlenbeck process which is defined as the solution of dX_t = (L(t) - alpha X_t)dt + delta dB_t and which is observed in continuous time. We derive an explicit representation of the generalized likelihood ratio test statistic assuming that the mean reversion function L(t) is a finite linear combination of known basis functions. In the case of a periodic mean reversion function, we determine the asymptotic distribution of the test statistic under the null hypothesis.

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Keywords

Time-inhomogeneous diffusion process, generalized likelihood ratio test, change point

Citation