Before revision:  We introduce a new saddlepoint density and tail area approximation to improve on the accuracy of the extant asymptotics. It features relative error of order O(m^{-1}) for m=n( T - 1 ) with n being the cross-sectional dimension and T the time-series dimension.
After revision:  We introduce a new saddlepoint density and tail area approximation feature relative error of order O(m^{-1}) for m=n( T - 1 ) with n being the cross-sectional dimension and T the time-series dimension.