We propose an algorithm to estimate the common density s of a stationary
process X1,...,Xn. We suppose that the process is either β or
τ-mixing. We provide a model selection procedure based on a generalization
of Mallows' Cp and we prove oracle inequalities for the selected estimator
under a few prior assumptions on the collection of models and on the mixing
coefficients. We prove that our estimator is adaptive over a class of Besov
spaces, namely, we prove that it achieves the same rates of convergence as in
the i.i.d framework