  The paper considers the problem of robust estimating a periodic function in a
continuous time regression model with dependent disturbances given by a general
square integrable semimartingale with unknown distribution. An example of such
a noise is non-gaussian Ornstein-Uhlenbeck process with the L\'evy process
subordinator, which is used to model the financial Black-Scholes type markets
with jumps. An adaptive model selection procedure, based on the weighted least
square estimates, is proposed. Under general moment conditions on the noise
distribution, sharp non-asymptotic oracle inequalities for the robust risks
have been derived and the robust efficiency of the model selection procedure
has been shown.
