New mixed AR(1)AR(1) time series models having approximated beta marginals

We consider the mixed AR(1)AR(1) time series model Xt={αXt−1+ξtw.p. p1βXt−1+ξtw.p. 1−p1,α,β,p1∈(0,1), where XtXt has twoparameter beta distribution B2(p,q),p,q>0. For parameters p=1,q>0;p=2,q>π2(2k+1)2,k∈N0;p=3,q≥(43π/6)3;p=4p=1,q>0;p=2,q>π2(2k+1)2,k∈N0;p=3,q≥(43π/6)3;p=4, q≥(3π/4)4q≥(3π/4)4 or p=5,q≥(9π/10)5p=5,q≥(9π/10)5 it is possible to calculate exact PDF which approximates beta distribution using analytical inversion of the Laplace transform.Using Laplace transform techniques and a suitable approximation procedure for the auxiliary Kummer function of the first kind, we prove that the innovation process has a mixed continuous distribution.We also consider estimation issues of the model.