danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8323-2024-68-4-271-281dan-1199Research ArticleМАТЕМАТИКАMATHEMATICSСтатистический анализ многомерных двоичных временных рядов на основе нейросетевой моделиStatistical analysis of multivariate binary time series based on a neural network modelХаринЮ. С.KharinYu. S.

Харин Юрий Семенович – академик, д-р физ.-мат. наук, профессор, директор

пр. Независимости, 4, 220030, Минск

Kharin Yuriy S. – Academician, D. Sc. (Physics and Mathematics), Professor, Director

4, Nezavisimosti Ave., Minsk, 220030

kharin@bsu.byШибалкоС. А.ShibalkoS. A.

Шибалко Сергей Анатольевич – студент

пр. Независимости, 4, 220030, Минск

Shibalko Siarhei A. – Student

4, Nezavisimosti Ave., Minsk, 220030

shibalko2003@bk.ruНИИ прикладных проблем математики и информатики БГУResearch Institute for Applied Problems of Mathematics and Informatics of the Belarusian State UniversityБелорусский государственный университетBelarusian State University202405092024684271281Copyright © Харин Ю.С., Шибалко С.А., 20242024Харин Ю.С., Шибалко С.А.Kharin Y.S., Shibalko S.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/1199

Рассматривается задача статистического анализа N-мерных двоичных временных рядов. Предлагается подход к решению этой задачи на основе малопараметрической нейросетевой модели эргодической цепи Маркова порядка s. Построены состоятельные статистические оценки параметров модели и алгоритмы компьютерного анализа данных с использованием нейросетевой модели: алгоритм оценивания параметров и алгоритм прогнозирования. Приведены результаты компьютерных экспериментов на модельных и реальных данных.

This article is devoted to the statistical analysis of multivariate binary time series. For solving this problem a parsimonious neural network model of Markov’s ergodic chain of order s was determined. Consistent statistical estimators for model parameters and estimation algorithms of parameters and forecasting algorithms of future states of time series were developed. The results of computer experiments on simulated and real data are presented.

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The authors declare that there are no conflicts of interest present.