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Cointegration describes the pattern that pairs of time series keep together in long run, although they diverge in short run. A generalisation of this behaviour is the fractional cointegration. Two statistical tests, the M – and ML–test are formulated for fractional cointegration in different situations. It turns out that the robust M–test reaches almost the same power as the maximum likelihood test under certain assumptions. In contrast to this, the power of the M–test is much higher than that of the ML–test if the examined time series is contami-nated following the general replacement model