Time series monotonic trend analysis

The problem of identifying changes in the characteristics of the time series under study during the observation period is considered. Almost always, the trend arises against the background of the statistical dependence of the elements of the time series. The dependence of individual observations becomes a nuisance factor. When constructing assumptions about changes, preference is given to models of a general nature: the trend of probabilistic characteristics is a monotonic function of an unknown form from the observation number (monotonic trend). The need to take into account the combination of both operating factors in the time series model and the need to obtain workable methods of data processing lead to the following scheme of actions: to take as a basis the already developed procedures, then, if possible, to adjust the conditions for their correct application to the required ones, and, finally, to use adapted options. The analysis of methods for processing the nuisance factor is carried out: neutralization of dependence, accounting for dependence, and generalization of the time series model. As an example, the problem of monitoring the stable operation of a two-processor task processing system with a random selection of the number of required processors is considered. The possibilities and limitations of the proposed methods are demonstrated.