We derive the relation between the biases of correlograms and of estimates of auto-regressive AR(k) representations of stationary series, and we illustrate it with a simple AR example. The new relation allows for k to vary with the sample size, which is a representation that can be used for most...

The present work applies saddlepoint approximation to calculate the left-hand tail of the distribution of the unit root t test and an asymptotic equivalent test under the null hypothesis of a unit root. (This is the tail of interest when testing against a stationary alternative.) The saddlepoint...