Multiplicative model the allocation of components of the time series

This paper is devoted to the substantiation of a multiplicative model of time series decomposition based on the axiomatic approach. In this model, the original time series is represented as a component-by-component product of the selected components. The components are described in the form of monomials. To determine the values of variable monomials, a function is minimized that measures deviations from the unit of all components of the product of the selected components from the values of the corresponding components of the original series. In the model under consideration, all the components of the original series and the selected components are positive numbers. Four requirements are formulated for methods of selecting components. It is proved that all these requirements are met if and only if the time series decomposition is performed by a multiplicative model. As an example, we consider a model for selecting trends and seasonal fluctuations from monthly series of efficient data.