Results of the analysis of requirements for methods for allocating time series components

The problem of method’s choosing for selecting components of a time series is considered. Such components can be a trend or periodic fluctuations (in particular, seasonal). The studied methods for selecting components are presented as a mapping of the original time series to the selected components. The requirements for these maps have been formulated: continuity, idempotency, additivity, and consideration of the informative nature of observations. In addition, we prove theorems that all the requirements are met by the decomposition into components of a time series using the least squares method. The selection of two components of a time series (trend and seasonal components) from quarterly and monthly data based on an additive model has been considered. The trend is defined as a polynomial of time, and seasonal fluctuations are defined as the sum of strictly periodic functions weighted by degrees of time. The presented additive model is applicable for analyzing the dynamics of stocks, production, transport, consumption of individual products in different areas, etc. It is more appropriate to use a multiplicative model for price dynamics, since indicators measured in relative rather than balance values are more stable. In this case, instead of the additivity requirement discussed in the article, it is necessary to introduce the multiplicativity requirement.