Методи прогнозування нестаціонарних часових рядів на основі двобічного експоненційного згладжування та оптимальної фільтрації

Розроблено методи оцінювання математичного сподівання прискорення зміни значень вибірки даних, їх застосовано для розробки адаптивних фільтрів Калмана та алгоритмів прогнозування на основі фільтра Калмана. Для відновлення пропущених значень, істинних закономірностей та прогнозування часових рядів розроблено методи двобічного експоненційного згладжування, ковзного двобічного експоненційного згладжування та адаптивного ковзного двобічного експоненційного згладжування. Розроблено методи відновлення пропущених значень та прогнозування для взаємозалежних часових рядів з використанням двобічного експоненційного згладжування. Розроблено інтегральний критерій адекватності моделі та критерій близькості. Створено систему підтримки прийняття рішень, в якій реалізовано традиційні та розроблені методи. The dissertation work is dedicated to development and application of applied scientific methodology of system analysis for solving actual tasks of restoring of missing values of time series, restoring true regularities of researched processes, forecasting of time series and performing automated processing of time series using created decision making support system. Methods of estimation of mathematical expectation of acceleration of values change of data samples using full and rarified samples of residuals of suboptimal filter with memory two were developed in this work. The best methods were selected between developed methods, they were used for development of adaptive Kalman filters. Adaptive Kalman filters showed better results in comparison to traditional methods in forecasting of daily average prices of zinc by the London metal exchange data. Method of estimation of mathematical expectation of acceleration of changes of time series values, which is changed based on the unknown law, using the exponential smoothing procedure to the constructed series of one-dependent pseudo-measurements of this parameter was developed. Forecasting algorithms based on Kalman filter were created using developed method. Created forecasting algorithms showed superiority in comparison to traditional methods by forecasting characteristics in forecasting of daily average prices of lead. Two-sided exponential smoothing method and algorithm for restoring of missing values of time series using this method were developed. The integral criterion of model adequacy was created. Application of the created method for restoring of true regularities and forecasting of time series was described. Created method showed superiority in comparison to traditional methods by statistical characteristics in restoring of daily average prices of zinc. Method for restoring missing values for mutually dependent time series using two-sided exponential smoothing was developed. This method showed superiority in comparison to traditional methods by statistical characteristics in restoring mutually dependent indices of sustainable development by the data of World data center. Method for forecasting of mutually dependent time series using two-sided exponential smoothing method was developed. This method showed superiority in comparison to exponential smoothing method in forecasting of sustainable development indices. Moving two-sided exponential smoothing method and algorithm for restoring of missing values of time series using this method were developed. This algorithm showed superiority in comparison to exponential smoothing method by statistical characteristics in restoring of monthly values of solar radio fluxes at a wavelength of 10.7 cm. The proximity criterion for estimation of models in restoring of the true regularities of time series evolution was developed. Moving two-sided exponential smoothing method showed better results in comparison to traditional methods in restoring of the true regularities and forecasting of solar data. Adaptive moving two-sided exponential smoothing method and algorithm for restoring of missing values of time series using this method were developed. Created method showed superiority in comparison to traditional methods in the restoring of missing values, true regularities and forecasting of solar data. Principles of system methodology were determined, which were used during development of decision making support system for organization, which is working on analysis and forecasting of time series. Architecture and structural scheme of part of analysis and forecasting of decision making support system were developed, different levels of access to this system were created according to departments for employees of this organization. Software implementation of decision making support system was performed, and description for its users was created. Opportunities of data analysis performing, traditional methods and created new methods of restoring of missing values, restoring of true regularities and forecasting of time series were implemented in the decision making support system. Examples of its using for work with financial-economic and solar data were provided. Разработаны методы оценивания математического ожидания ускорения изменения значений выборки данных, они применены для разработки адаптивных фильтров Калмана и алгоритмов прогнозирования на основе фильтра Калмана. Для восстановления пропущенных значений, истинных закономерностей и прогнозирования временных рядов разработаны методы двустороннего экспоненциального сглаживания, скользящего двустороннего экспоненциального сглаживания и адаптивного скользящего двустороннего экспоненциального сглаживания. Разработаны методы восстановления пропущенных значений и прогнозирования для взаимозависимых временных рядов с использованием двустороннего экспоненциального сглаживания. Разработаны интегральный критерий адекватности модели и критерий близости. Создана система поддержки принятия решений, в которой реализованы традиционные и разработанные методы.