  In this paper we study periodical stochastic processes, and we define the
conditions that are needed by a model to be a good noise model on the
circumference. The classes of processes that fit the required conditions are
studied together with their expansion in random Fourier series in order to
provide results about their path regularity. Finally, we discuss a simple and
flexible parametric model with prescribed regularity that is used in
applications, and we prove the asymptotic properties of the maximum likelihood
estimates of model parameters.
