Additive mathematical model of gas consumption process

Abstract

The problem of construction of a new mathematical model of the gas consumption process is considered in this paper. The new mathematical model is presented as an additive mixture of three components: cyclic random process, trend component and stochastic residue. The process of obtaining three components is carried out on the basis of caterpillar method, thus obtaining ten components of singular decomposition. In this approach, the cyclic component is formed from the sum of nine components of the schedule, which have one thing in common – repeated deployment over time. The trend component of the new mathematical model is the second component of singular decomposition, and the stochastic residue is formed on the basis of the difference between the values of the studied gas consumption process and the sum of cyclic and trend components. Two approaches to stochastic processing of cyclic gas consumption process based on the known model of stochastic-periodic random process and cyclic random process as models of the cyclic component are used in this paper. Application of mathematical model of cyclic component in the form of cyclic random process with cyclic structure makes it possible to obtain estimation of variance on cycle of gas consumption process, provided segmentation of cyclic component on depressions, much less in comparison of obtained variance estimation for indicating greater accuracy in the study of the gas consumption process and will use the obtained stochastic estimates when modeling the gas consumption process in further studies.