Линейная авторегрессия со случайными коэффициентами на основе метода группового учёта аргументов в условиях квазиповторных наблюдений

Abstract

Предложен критерий регулярности с разбиением выборок наблюдений на обучающие и проверочные подвыборки в условиях квазиповторных наблюдений для моделирования в классе авторегрессионных уравнений со случайными коэффициентами. Выявлено условие редукции оптимальной авторегрессионной модели, которое зависит от параметров модели и объемов выборок.

Запропоновано критерій регулярності з розбиттям вибірок спостережень на навчальні та перевірні підвибірки за умов квазіповторних спостережень для моделювання в класі авторегресійних рівнянь з випадковими коефіцієнтами. Виявлено умову редукції оптимальної авторегресійної моделі, що залежить від параметрів моделі і обсягів вибірок.

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.