A Multiplicative Model for the Identification of Time Series Components
V. I. Zorkaltsev, Marina Polkovskaya · Numerical Analysis and Applications · 2022
Abstract This paper is devoted to a substantiation of a multiplicative model of time series decomposition based on an axiomatic approach. In this model, a given time series is presented as a component-by-component product of the components to be identified. The components are described in the form of monomials. To determine the values of the variable monomials, a function is minimized that measures deviations from unity of all components of the product of the components to be identified from the values of the corresponding components of the original series. In the model under consideration, all components of the original series and the components to be identified are positive numbers. Four requirements are formulated for the methods of identifying the 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 identifying the trends and the seasonal fluctuations from monthly series of economic data.