The paper considers the problem of robust estimating a periodic function in a continuous time regression model with the dependent disturbances given by a general square integrable semimartingale with an unknown distribution. An example of such a noise is a non-Gaussian Ornstein-Uhlenbeck process with jumps (see (

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 L 2 -risk (oracle inequality) has been derived under mild conditions on the noise. For the OrnsteinUhlenbeck 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.

This paper considers the problem of estimating parameters in a periodic regression in continuous time with a semimartingale noise by discrete time observations. Improved estimates for the regression parameters are proposed. It is established that under some general conditions these estimates have an advantage in the mean square accuracy over the least squares estimates. The asymptotic minimaxity of the improved estimates has been proved in the robust risk sense. The properties of the proposed procedure for the models with non-Gaussian noises of pulse type have been studied. The pulse disturbances have random intensity and occur at random times which form a Poisson process.

We consider the problem of parameter estimation for multidimensional continuous-time linear stochastic regression models with an arbitrary finite number of unknown parameters and with martingale noise. The main result of the paper claims that the unknown parameters can be estimated with prescribed mean-square precision in this general model providing a unified description of both discrete and continuous time process. Among the conditions on the regressors there is one bounding the growth of the maximal eigenvalue of the design matrix with respect to its minimal eigenvalue. This condition is slightly stronger as compared with the corresponding conditions usually imposed on the regressors in asymptotic investigations but still it enables one to consider models with different behavior of the eigenvalues. The construction makes use of a two-step procedure based on the modified least-squares estimators and special stopping rules.

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