On Darling-Robbins type confidence sequences and sequential tests with power one for parameters of an autoregressive process

In this paper, we have obtained confidence sequences using Chow's generalization of Hájek-Rényi inequality and the law of iterated logarithm for the autoregressive parameter in a stable first order autoregressive model where innovations are assumed to be independently and identically distributed. A sequential testing procedure with power one has also been proposed. We have also indicated a generalization to confidence sequences for several parameters in a pth order autoregressive model.