A semimartingale driven continuous time linear regression model is studied. Assumptions concerning errors allow us to consider also models with infinite variance. The order of the almost sure convergence of a class of estimates which includes least squares estimates is given. In the presence of...

For a d-dimensional gaussian martingae M with tensor increasingprocess we prove that <M>+tMt converges in Rd with probability 1 as t --> [infinity] and the limit is zero a.s. iff tr <M>+t tends to zero. We apply this result to study the strong consistency of estimates in a linear regression model.

Multiple linear regression models with non random regressors in continuous time are considered. The strong consistency of least squares estimates is established under minimal assumptions on the design when the process of errors is a semimartingale satisfying some regularity condition.

A law of iterated logarithm and a large deviation type result are established for multidimensional Gaussian martingales. An application to the asymptotic study of estimates in a normal regression model is discussed.

The maximum likelihood estimation of the parameters of a complex-valued zero-mean normal stationary first-order autoregressive process is investigated. It is shown that the likelihood function corresponding to independent replicated series is uniquely maximized at a point in the interior of the...