Construction leading indicators using differentiators

Abstract

The problem of constructing leading indicators of economic processes is considered. These indicators provide information about the beginning of the trends that have not yet explicitly demonstated themselves. The scientific novelty of the research conducted in this article is that the task of constructing leading indicators is reduced to the task of automatic forecasting of a certain class of signals, i.e. to the task of synthesizing an automatic predictor of a certain class of signals. The tasks of synthesis of automatic predictors arise both in the theory of automatic control and in various applications where it is required to obtain a forecast for the observed implementation. The class of signals considered in the article is quite wide. The synthesis of automatic predictors is carried out using differentiating devices: the exponential transfer function is decomposed into the Burman — Lagrange series by degrees of the transfer function of the differentiating link being implemented to solve the problem. The approximated transfer function is transcendental and infinite-dimensional. The Burman — Lagrange expansion allows the regularization of an incorrect problem. Accuracy of the prediction can be increased due to the regularization parameter, as well as by increasing the number of terms of the Burman — Lagrange series. The results of modeling the leading indicator constructed with the help of an automatic forecast are presented. A comparison of the leading indicator constructed in the article with indicators widely used in practice which were built on the basis of the Kalman filter and the Savitsky — Goley filter and it shows good accuracy in predicting the trend of the economic process. The proposed method of constructing leading indicators can be used to predict economic processes, to make informed investment decisions and timely rebalancing of the investment portfolio.