FRACTIONAL COINTEGRATING REGRESSION IN THE PRESENCE OF LINEAR TIME TRENDS

Uwe Hassler, Francesc Marmol and Carlos Velasco

No 138, Computing in Economics and Finance 2000 from Society for Computational Economics

Abstract: 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.

Date: 2000-07-05
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Working Paper: Fractional cointegrating regressions in the presence of linear time trends (1998)
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