Suppose that the Ordinary Least Squares regressors X follow a vector Ornstein-Uhlenbeck process, with growth matrix bA. The limiting sample variance matrix V is of interest. If A=kI, k[greater-or-equal, slanted]0, then [not partial differential]V/[not partial differential]b[greater-or-equal,...

Recent experimental results presented in Burridge and Taylor (2001a,b, and 2003) show that, as usually implemented, the Hylleberg et al. (1990) seasonal unit root tests can be rather liberal, with true level often substantially higher than nominal level. This effect is due to the presence of any...

We obtain an inequality for th esmaple varaince of a Brownian motion on [0,1] and an associated Ornstein-Uhlenbeck process. The result is applied to a regression involving a near-integrated regressor, and establishes that in the limit the dispersion of the least squares estimator is greater in...

In this paper, we analyse the behaviour of regression-based tests for seasonal unit roots when the error is periodically heteroscedastic. We show, using the case of quaterly data to illustrate, that the limiting null distribution of tests for unit roots at the zero and Nyquist frequencies are...