  This paper considers the problem of estimating a periodic function in a
continuous time regression model with an additive stationary gaussian noise
having unknown correlation function. A general model selection procedure on the
basis of arbitrary projective estimates, which does not need the knowledge of
the noise correlation function, is proposed. A non-asymptotic upper bound for
quadratic risk (oracle inequality) has been derived under mild conditions on
the noise. For the Ornstein-Uhlenbeck noise the risk upper bound is shown to be
uniform in the nuisance parameter. In the case of gaussian white noise the
constructed procedure has some advantages as compared with the procedure based
on the least squares estimates (LSE). The asymptotic minimaxity of the
estimates has been proved. The proposed model selection scheme is extended also
to the estimation problem based on the discrete data applicably to the
situation when high frequency sampling can not be provided.
