We consider the construction of valid Edgeworth expansions for statistics arising in the context of Gaussian autoregression. By exploiting the properties of exponential families (to which these models belong), validity, of any order, is routinely established for a wide class of statistics.

Via the leading unit-root case, the problem of testing on a lagged dependent variable is characterized by a nuisance parameter which is present only under the alternative [see Andrews and Ploberger, Econometrica (1994) Vol. 62, pp. 1318-1414]. This has proven to be a barrier to the construction...

This paper provides a (saddlepoint) tail probability approximation for the distribution of an optimal unit root test. Under restrictive assumptions, Gaussianity, and known covariance structure, the order of error of the approximation is given. More generally, when innovations are a linear...