Change point testing for the drift parameters of a periodic mean reversion process
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Date
2012-11-05
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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