ИДЕНТИФИКАЦИЯ ПАРАМЕТРОВ ARFIMA МОДЕЛИ ФРАКТАЛЬНОГО ПРОЦЕССА
Електронний архів E-archive DonNTU – (Electronic archive Donetsk National Technical University)
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| Title |
ИДЕНТИФИКАЦИЯ ПАРАМЕТРОВ ARFIMA МОДЕЛИ ФРАКТАЛЬНОГО ПРОЦЕССА
Identification of ARFIMA Model’s Parameters for Fractal Process Ідентифікація параметрів ARFIMA моделі фрактального процесу |
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| Creator |
Дегтяренко, И.В.
Гарматенко, А.М. Ярошенко, О.А. Degtyarenko, I.V. Garmatenko, A.M. Yaroshenko, O.A. Дегтяренко, І.В. Гарматенко, О.М. |
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| Subject |
фрактальний процес
ARFIMA показник Херста прогностична модель Detrended Fluctuation Analysis fractal process Hurst parameter predictive model фрактальный процесс показатель Херста прогностическая |
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| Description |
The questions of developing a predictive model for fractal process are considered. Self-similarity and long-term memory are inherent for fractal processes. This is the basis for building predictive models of these processes. The general concept of developing a predictive ARFIMA model is described in the article. The interrelation of the parameters of ARFIMA model with fractal properties of the process is analyzed. The recommendations for the practical application to describe stationary processes within longterm memory are examined in the article. The procedure for calculating the parameter d of ARFIMA models using Whittle is described. A new method of determining this parameter is based on calculating the Hurst parameter using “Detrended Fluctuation Analysis” is described. This method provides the most stable and adequate Hurst parameter estimation for fractal processes. The dependences of Hurst calculation accuracy parameters and average interval of correlation with the length of data’s window are analyzed. The recommendations about selection of the minimum length of data’s window are given. The efficiency of the proposed method is evaluated by numerical simulation. Two prediction models of fractal process were constructed. The parameter d of first ARFIMA model was calculated by Whittle method. The parameters of the second model were calculated by the proposed method. The method of the relative error of approximation was used in assessing the quality of prediction. The simulation results showed that the developed method increases the horizon of forecasting fractal process by 6% in comparison with application of the classical approach, based on the method of Whittle. В статье рассмотрены вопросы построения прогностической ARFIMA модели фрактального процесса. Проведен анализ взаимосвязи параметров ARFIMA модели с показателем Херста. Описана методика определения параметров данной модели на основе использования метода «Detrended Fluctuation Analysis». Исследована эффективность применения данной методики при построении прогностических моделей. |
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| Date |
2013-09-20T10:57:45Z
2013-09-20T10:57:45Z 2013 |
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| Type |
Article
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| Identifier |
Наукові праці Донецького національного технічного університету. Серія: Обчислювальна техніка та автоматизація. Випуск 2 (25). - Донецьк, ДонНТУ, 2013. С - 111-119
2075-4272 УДК 519.216 http://ea.donntu.edu.ua/handle/123456789/22812 |
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| Publisher |
Донецький національний технічний університет
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