## Control Systems and Computers, N1, 2016, Article 1

Upr. sist. maš., 2016, Issue 1 (261), pp. 3-15.

UDC 519.25:681.5

Sarychev Alexander P., Doctor (Eng.), Institute of techn. mechanics of NAS and NCA of Ukraine (Dnepropetrovsk), E-mail: Sarychev@prognoz.dp.ua

### Linear Autoregression with Random Coefficients Based on the Group Method of Data Handling in Conditions of Quasirepeated Observations

Introduction and purpose: The linear autoregression equation is traditional mathematical object in the theory and practice of the Group Method of Data Handling (GMDH). In 80-th years of the last century academician O.G. Ivakhnenko often posed such tasks in connection with so-called “the objective system analysis (OSA)” and then, as a rule, as criterion of selection of models (parameter of quality of regression equation) the criterion of regularity of GMDH was applied. The developed criterion is the criterion of regularity which is constructed with dividing of observations on training and testing subsamples in conditions of quasirepeated observations.

Methods: Object of research is process of modelling in a class of autoregression equations in conditions of uncertainty on structure of regressors. In this theoretical article we used the multivariate statistical analysis, the regression analysis, the theory of matrixes, the mathematical analysis and the Group Method of Data Handling.

Results: For modeling in a class of autoregression equations the criterion of regularity with dividing of observation sample on training and testing subsamples in conditions of quasirepeated observations is offered. It is proved, that the optimum set of regressors exists. The condition of a reduction of optimal autoregression equation is obtained. This condition depends on parameters of autoregression equation and volumes of samples.

Conclusion: The developed criterion of regularity allows solving a problem of structural identification in a class of autoregression equations in conditions of quasirepeated observations and can be recommended at the decision of various scientific and practical problems.

Keywords: structural uncertainty, criterion of regulatory, autoregression, GMDH.

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Recieved 09.04.2015