Autoregressive – spectrally integrated moving average model
DOI:
https://doi.org/10.15587/2312-8372.2014.21699Keywords:
time series forecasting, structural identification, the Box-Jenkins method, the "Caterpillar''-SSA methodAbstract
The class synthesis of mathematical models, based on sharing ideas of two methods, which in separate are viewed skeptically by many experts of the prediction field, is carried out. However, they are well substantiated theoretically. The first method is a deterministic method of different types of analysis and prediction, which has not been included in the standard mathematical software yet, i.e. the "Caterpillar''-SSA method. The second one is a statistical method, i.e. the Box-Jenkins method. The model of autoregression, namely spectrally integrated moving average, is proposed. This model implements a trend approach, which lies in modeling the process as a deviation of actual values of a relative trend component and leads to synergy, mutually compensating the opposite in nature disadvantages of its model components. The proposed ARSIMA model identifies the long-term process dependence only by two parameters. This model has a wide range of application.References
- Бокс, Дж. Анализ временных рядов, прогноз и управление [Текст]: пер. с англ. / Дж. Бокс, Г. Дженкинс; под ред. В. Ф. Писаренко. – М.: Мир, 1974. – Кн. 1. – 406 с.
- Бокс, Дж. Анализ временных рядов, прогноз и управление [Текст]: пер. с англ. / Дж. Бокс, Г. Дженкинс; под ред. В.Ф. Писаренко. – М.: Мир, 1974. – Кн. 2. – 197 с.
- Безрукова, Е. Г. Прогнозирование статистических временных рядов [Текст]: учеб. пос./ Е. Г. Безрукова, Е. А. Руденчик. – Ярославль: Яросл. гос. техн. ун-т, 1997. – 94 с.
- Евдокимов, А. Г. Оперативное управление потокораспределением в инженерных сетях [Текст] / А. Г. Евдокимов, А. Д. Тевяшев. – Х. : Вища школа, 1980. – 144 с.
- Седов, А. В. Моделирование объектов с дискретно-распределёнными параметрами: декомпозиционный подход [Текст] / А. В. Седов. – Южный научный центр РАН. – М. : Наука, 2010. – 438 с.
- Бэнн, Д. В. Сравнительные модели прогнозирования электрической нагрузки [Текст]: пер. с англ. / Д. В. Бэнн, Е. Д. Фармер. – М.: Энергоатомиздат, 1987. – 200 с.
- Andersson, M. K. On the Effects of Imposing or Ignoring Long Memory When Forecasting [Text] / M. K. Andersson // Working Paper Series in Economics and Finance. – 1998. – T. 225. – P. 1-14.
- Hosking, J. R. M. Fractional differencing [Text]/ J. R. M. Hosking // Biometrika. – 1981. – Vol. 68, No. 1. – P. 165-176.
- Голяндина, Н. Э. Метод «Гусеница»-SSA: прогноз временных рядов [Текст]: учеб. пособие / Н. Э. Голяндина. – СПб.: С.-Петербургский государственный университет, 2004. – 52 с.
- Горелова, В. Л. Основы прогнозирования систем [Текст]: учеб. пособ. для инж.-экон. спец. вузов / В. Л. Горелова, Е. Н. Мельникова – М.: Высш. шк., 1986. – 287 с.
- Boks, J., Dzhenkins, H.; In: Pisarenko, V. F. (1974). Analiz vremennykh riadov, prohnoz i upravlenie. Book 1. M.: Mir, 406.
- Boks, J., Dzhenkins, H.; In: Pisarenko, V. F. (1974). Analiz vremennykh riadov, prohnoz i upravlenie. Book 2. M.: Mir, 197.
- Bezrukova, E. H., Rudenchik, E. A. (1997). Prohnozirovanie statisticheskikh vremennykh riadov. Yaroslavl': Yarosl. hos. tekhn. un-t, 94.
- Evdokimov, A. H., Teviashev, A. D. (1980). Operativnoe upravlenie potokoraspredeleniem v inzhenernykh setiakh. Kh.: Vishcha shkola, 144.
- Sedov, A. V. (2010). Modelirovanie obiektov s diskretno-raspredelionnymi parametrami: dekompozitsionnyi podkhod. Yuzhnyi nauchnyi tsentr RAN. M.: Nauka, 438.
- Benn, D. V., Farmer, E. D. (1987). Sravnitel'nye modeli prohnozirovaniia elektricheskoi nahruzki. M.: Enerhoatomizdat, 200.
- Andersson, M. K. (1998). On the Effects of Imposing or Ignoring Long Memory When Forecasting. Working Paper Series in Economics and Finance, T. 225, 1-14.
- Hosking, J. R. M. (1981). Fractional differencing. Biometrika, Vol. 68, No. 1, 165-176.
- Holiandina, N. E. (2004). Metod «Husenitsa»-SSA: prohnoz vremennykh riadov. SPb.: S.-Peterburhskii hosudarstvennyi universitet, 52.
- Horelova, V. L., Mel'nikova, E. N. (1986). Osnovy prohnozirovaniia sistem. M.: Vyssh. shk., 287.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 Виталий Николаевич Щелкалин
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.