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Climatic time series, in general, and hydrological time series, in particular, exhibit pronounced annual periodicity. This periodicity and its corresponding harmonics affect the nonlinear properties of the relevant time series (i.e. the long-term volatility correlations and the width of the Multifractal spectrum multifractal spectrum) and thus have to be filtered out before studying fractal and volatility properties. We compare several filtering techniques and find that in order to eliminate the periodicity effects on the nonlinear properties of the hydrological time series, it is necessary to filter out the seasonal standard deviation in addition to the filtering of the seasonal mean, with conservation of linear two-point correlations Correlation linear two-point . We name the proposed filtering technique ˵phase substitution″, because it employs the Fourier phases of the series. The obtained results still indicate nonlinearity of the river data, its strength being weaker than under previously used techniques. [ABSTRACT FROM AUTHOR]