  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 $dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t$, 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.
