Linear stochastic distributed model of moneyaccumulation in the form of a state space

Abstract

The article deals with the problem of the passive parametric identification of systems for modeling the evolution of money savings income and expenses of one household using a linear stochastic distributed model in the form of a state space taking into account white noises model of the investigated object dynamics’ and white noises of the linear model measuring system of a distributed type. The use of the finite difference method allowed reducing the solution of partialdifferential equations to the solution of linear finite difference system with private derivatives to be reduced to the solution of a system of linear finite-difference and algebraic equations represented by models in the form of state space. It was proposed the use of a Kalman filtering algorithm for reliable evaluation of object behavior. The statement of the problem of estimating the coefficients of the equation of evolution of money savings income and expenses of one household is given. The structure of household income and expenses is described, taking into account additional additive white noise meters. An algorithm for numerical approbation of method for solving the problem of estimating the coefficients of an equation in the form of the state space for the evolution of money savings income and expenses of one household is considered. Calculations were carried out using the Matlab mathematical system based on statistical data for five years, taken from the site “Agency for Strategic planning and reforms of the Republic of Kazakhstan Bureau of National statistics”. The proposed method for solving the problem of coefficients assessment’s passive identification using the equations of money savings for one household in the form of a state space is sufficiently universal. Key words: linear finite-difference equation, model in the form of a state space, evolution of one household money savings, passive identification, Kalman filter, prediction estimates, filtering estimates.