The influence of the periodic signals in time series on the Hurst parameter estimate is investigated with temporal, spectral and time-scale methods. The Hurst parameter estimates of the simulated periodic time series with a white noise background show a high sensitivity on the signal to noise ratio and for some methods, also on the data length used. The analysis is then carried on to the investigation of extreme monthly river flows of the Elbe River (Dresden) and of the Rhine River (Kaub). Effects of removing the periodic components employing different filtering approaches are discussed and it is shown that such procedures are a prerequisite for an unbiased estimation of H. In summary, our results imply that the first step in a time series long-correlation study should be the separation of the deterministic components from the stochastic ones. Otherwise wrong conclusions concerning possible memory effects may be drawn.