SADDLEPOINT APPROXIMATION FOR THE LEAST-SQUARES ESTIMATOR IN FIRST-ORDER AUTOREGRESSION

Phillips (1978) extended Daniels' (1956) approximation to the density of a modified correlation coefficient to obtain a saddlepoint approximation to the density of the least squares estimator in the first order noncircular autoregression. The resulting approximation is undefined in a substantial part of the tails. In this note, we establish that a suitable deformation of the contour of integration leads to a different type of saddlepoint approximation defined everywhere on the support of the density. The relative error of this approximation is bounded in the extreme tails.