Adaptation of stochastic model of economic cycles to empiric data

Abstract

This paper deals with adaptation of the stochastic model of the economic cycle, represented by the values of the gross product. Establishing the statistical equivalence of the Yule series to discrete samples of income oscillations made it possible to determine analytical expressions between the coefficients of the Yule model and the parameters of economic cycle. This, the adaptation of the cycle model to empirical data is reduced to the linear problem of estimating the Yule model factors. The peculiarity of solution to this problem ensures the presence of an optimal discretization of the income function in the form of four samples for the cycle period. It is shown that with such discretization, the highest accuracy of calculated parameter estimates is ensured, that is, the efficiency of the estimates is obtained. The proposed procedure for adapting the cycle models considers the features of the economic data and provides: 1) recovery of the income function from values of the gross product estimates; 2) extraction of values of a cycle under interest from the recovered data; 3) determination of the time interval of cycle pseudo-stationarity; 4) parameter estimation of the cycle model; 5) accuracy analysis of parameter estimates. The procedure is formally (mathematically) described from the empirical values of the gross product to getting estimates of cycle parameters. It is applicable for econometric problems of estimating the parameters of systems described by ordinary differential and difference equations of the second order.