Аннотация:The paper presents a methodology for the stochastic analysis of random processes based on the method of moving separation of finite normal mixtures. Within the framework of our approach, the one-dimensional distributions of observed processes are approximated by finite location-scale mixtures of normal distributions. The theoretical background of these models is based on that finite normal mixtures are convenient approximations to general location-scale normal mixtures or normal variance-mean mixtures which are limit laws for the distributions of sums of a random number of independent random variables or non-homogeneous and non-stationary random walks and hence, are reasonable asymptotic approximations to the statistical regularities in observed real processes. We show that this approach can be also applied to positive time series, if the initial data is primarily noised by adding i.i.d. normal random variables with known parameters. This approach allows to analyze the regularities in the variation of the parameters and capturing the low-term variability in the case of complex internal structure of data.