Asymptotic distribution theory for some test statistics in autoregressive and Galton-Watson processes

Abstract: In this thesis, we study asymptotic distributions of some unit root test statistics in autoregressive processes. We then generalize, at first to the situation when the true parameter value is close to one^(thenear integrated case), and secondly to the corresponding test problems in the Galton-Watson process (i.e. 'the branching process with immigration). The main tools used are Feynman-Kac’ formula, to obtain asuitable Laplace transform, together with saddlepoint approximation in the Fourier inversion formula.