On mixed AR(1) time series model with approximated beta marginal

We consider the mixed AR(1) time series model when Xt has the two parameter beta distribution , p[set membership, variant](0,1],q>1. Special attention is given to the case p=1 when the marginal distribution is approximated by the power law distribution closely connected with the two parameter Kumaraswamy distribution . Using the Laplace transform technique, we prove that for p=1 the distribution of the innovation process is uniform discrete. For p[set membership, variant](0,1), the innovation process has a continuous distribution. We also consider estimation issues of the model.