FRACTIONAL COINTEGRATING REGRESSION IN THE PRESENCE OF LINEAR TIME TRENDS

We consider regressions of nonstationary fractionally integrated variables dominated by linear time trends. The regression errors can be short memory, long memory, or even nonstationary, and hence allow for a very flexible cointegration model. Our main contributions are two: First, we analyze the limiting behaviour of the regression estimators. We find in case of simple regressions that limiting normality arises at a rate of convergence that is independent of the order of integration of the regressor. This result does not carry over to the multivariate case, where the limiting distribution is more complicated. Second, we investigate a residual-based, log-periodogram regression. We state conditions that allow consistent estimation of the memory parameter of the error term. This estimator follows a limiting normal distribution and is therefore suitable for cointegration testing. The applicability of this asymptotic result to finite samples is established by means of Monte Carlo experiments.