The correlations within the time series of the seismic electric signal (SES) activities have been studied in a previous paper [P. Varotsos, N. Sarlis, and E. Skordas, Phys. Rev. E 66, 011902 (2002)]. Here, we analyze the time series of successive high- and low-level states' durations. The existence of correlation between the states is investigated by means of Hurst and detrended fluctuation analysis (DFA). The multifractal DFA (MF-DFA) is also employed. The results point to a stronger correlation, and hence longer memory, in the series of the high-level states. Furthermore, an analysis in the "natural" time domain reveals that certain power spectrum characteristics seem to distinguish SES activities from "artificial" (man-made) electric noises. More precisely, for natural frequencies 0<phi<0.5, the curves of the SES activities and artificial noises lie above and below, respectively, that of the "uniform" distribution (UD). A classification of these two types of electric signals (SES activities, artificial noises), cannot be achieved on the basis of the values of the power-law exponents alone, if the Hurst analysis, DFA, and MF-DFA are applied to the original time series. The latter two methods, however, seem to allow a distinction between the SES activities and artificial noises when treating them (not in conventional the time frame, but) in the natural time domain. To further test the techniques, a time series produced by another system was examined. We chose a signal of ion current fluctuations in membrane channels (ICFMCs). The following conclusions, among others, have been obtained: First, the power spectrum analysis in the natural time domain shows that the ICFMC curve almost coincides (in the range 0<phi<0.5) with that of the UD, and hence ICFMC lies just in the boundary between the SES activities and artificial noises. Second, MF-DFA indicates monofractality for the ICFMCs with a generalized Hurst exponent h=0.84+/-0.03 in the range 7-70 ms.