This chapter examines the problems of dealing with trending type data when there is uncertainty over whether or not we really have unit roots in the data. This uncertainty is practical – for many macroeconomic and financial variables theory does not imply a unit root in the data however unit...

This paper derives the asymptotic power envelope for tests of a unit autoregressive root for various trend specifications and stationary Gaussian autoregressive disturbances. A family of tests is proposed, members of which are asymptotically similar under a general 1(1) null (allowing...

It is well known that the distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice the order of integration is rarely blown. This paper examines two conventional approaches to this...

We derive the family of tests for a unit root with maximal power against a point alternative when an arbitrary number of stationary covariates are modeled with the potentially integrated series. We show that very large power gains are available when such covariates are available. We then derive...