AR(1) time series with approximated Beta marginal

We consider the AR(1) time series model Xt ? ?Xt?1 = ?t, ??p ? N \ {1}, when Xt has Beta distribution B(p, q), p ? (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 Kumaraswamy distribution Kum(p, q), p ? (0, 1], q > 1. Using the Laplace transform technique, we prove that for p = 1 the distribution of the innovation process is uniform discrete. For p ? (0, 1), the innovation process has a continuous distribution. We also consider estimation issues of the model. nema