The limiting distribution of the normalized autocorrelation coefficient in the case of a unit root is given in a closed form. It is found that high order transcendental functions such as the parabolic cylinder functions are indispensable to express this distribution, thus departing from the...

A new formula for the mean squared error of a unit root estimator is derived. Its minimization gives rise to an estimator which is almost unbiased, unlike the maximum likelihood estimator. For this reason, it is suggested that the problem of testing for unit roots may be solved more...

A unified framework to derive the distribution of conventional statistics under a unit root is presented. It is based on formulae which can generate (analytically as well as numerically) the densities and distributions of statistics such as the t ratio, the normalized autocorrelation...

We derive formulae for the asymptotic density and distribution functions of the t-statistic for autoregressive unit roots based on M-estimators. The distribution depends upon a nuisance parameter. Consequently, new critical values for this test have to be generated for each new estimator that is...

We derive formulae for the asymptotic density and distribution functions of the t-statistic for autoregressive unit roots based on M-estimators. The distribution depends upon a nuisance parameter. Consequently, new critical values for this test have to be generated for each new estimator that is...

We propose a class of statistics where the direction of one of the alternatives is incorporated. It is obtained by modifying a class of multivariate tests with elliptical confidence regions, not necessarily arising from normal-based distribution theory. The resulting statistics are easy to...