This article presents the results the adapted complex methodology operation for the pre-estimating analysis of the dynamics of tourist flow time series decomposition in the Dombai ski village, the features of which are in the combined use of both classical and new “nonlinear” statistics. The methods proposed and tested by the authors are presented in the form of a pre-estimating model for assessing the tourist flow time series trend stability. The following methods of nonlinear dynamics were tested: the method of the normalized Hurst range, phase-plane analysis. The methods of fractal analysis used and adapted by the authors ensure the identification and assessment of a number of socio-economic time series fundamental qualitative and quantitative pre-estimating characteristics, namely, the presence of memory, including long-term memory, its depth, which in turn can determine the process as persistent (antipersistent, trend-resistant or reverse) to reveal the noise color.