Developing of approaches for the unhomogeneus time series analysis based on statistical characteristics
DOI:
https://doi.org/10.15587/1729-4061.2014.28014Keywords:
non-homogeneous components, non-stationary time series, statistical characteristics, risk assessment, forecastingAbstract
In this paper, a study of non-homogeneous time series, as a special case of a class of non-stationary time series, which are not given to stationary by integrating the 1st and 2nd order was carried out. Because of the presence of non-homogeneous components, time series is characterized by a non-linear trend, periodic components with variable amplitude, as well as a non-permanent structure. A method for identifying the series of this class based on statistical characteristics, using statistical tests and criteria was proposed. This method allows reasonable approach to selecting a method for forecasting a number of changes with respect to all the hidden features of the original data, as well as the reasons and assumptions of various forecasting methods. For example, in the construction of forecasting models of the non-homogeneous time series using statistical forecasting methods, such as AR (p), MA (q), ARMA (p, q), AR (p) + linear trend, ARCH (p), GARCH (p, q), SV (p), is inadequate in view of violating the requirements for applying these methods, in particular time invariance. An adaptive approach for forecasting non-homogeneous time series based on the method of singular spectrum analysis and presentation of time series in several phase spaces is proposed in the paper.
Another problem in forecasting the time series is a risk assessment in decision-making based on the forecasting model. A method for estimating the maximum level of losses in forecasting non-homogeneous time series with a given probability was developed in the paper. A confidence interval of forecasting non-homogeneous time series of exchange rates, which allows estimating the adoption of one or other solutions depending on the amount of the transaction was built.
The results obtained in this paper can be used for a sound approach to the selection of a forecasting method in automated systems, as well as in the evaluation of making management decisions.
References
Shamsha, B. V., Neguritsa, D. S., Chistiakova, A. A. (2009). Informatsionnaia tehnologiia otsenki statisticheskih harakteristik vremennyh riadov kursa valiuty. Novye tehnologii, № 2 (24), 43-48.
Box, G. E. P., Jenkins, G. M., Reinsel, G. C. (2008). Time Series Analysis: Forecasting and Control. Ed. 4. US: John Wiley & Sons., 784.
Brillindzher, D. (1980). Vremennye riady. Obrabotka dannyh i teoriia. M.: Mir, 536.
Kil'dishev, G. S., Frenkel', A. A. (1973). Analiz vremennyh riadov i prognozirovanie. M.: Statistika, 104.
Ayvazian, S. A., Mhitarian, V. S. (1998). Prikladnaia statistika i osnovy iekonometriki. M.: YuNITI, 1006.
Ruelle, D., Takens, F. (1971). On the nature of turbulence. Communications in Mathematical Physics, Vol. 20, №. 3, 167-192. Available: http://projecteuclid.org/euclid.cmp/1103857186.
Golyandina, N., Nekrutkin, V., Zhigljavsky, A. (2001). Analysis of Time Series Structure: SSA and Related Techniques. Boca Raton: Chapman & Hall/CRC, 320.
Danilov, D. L., Zhigliavskiy, A. A. (1997). Glavnye komponenty vremennyh riadov: metod “Gusenitsa”. SPb.: SpbGU, 150.
Solntsev, V. N., Danilov, D. L., Zhigliavskii, A. A. (1997). Glavnye komponenty vremennyh riadov: Metod “Gusenitsa”. SPb.: “PRESSKOM”, 48-72.
Goliandina, N. Ye. (2004). Metod «Gusenitsa»-SSA: analiz vremennyh riadov. SPb.: SPbGU, 74.
Golyandina, N., Zhigljavsky, A. (2013). Singular Spectrum Analysis for Time Series. SpringerBriefs in Statistics. Springer Berlin Heidelberg, 120. doi:10.1007/978-3-642-34913-3.
Hassani, H. (2007). Singular Spectrum Analysis: Methodology and Comparison. Journal of Data Science, Vol. 5, No. 2, 239-257. Available: http://mpra.ub.uni-muenchen.de/id/eprint/4991.
Engel, J., Gizicki, M. (1999). Conservatism, accuracy and efficiency: Comparing Value at Risk methods. Discussion paper 2. Australia: Australian Prudential Regulation Authority, Reserve Bank of Australia, 64.
Longerstaey, J., Spenser, M. (1996). RiskMetrics technical document. Ed. 4. New York: J.P. Morgan/Reuters, 281.
Lushavin, A. P. (2012). Obrabotka vremennyh riadov parametrov tehnologicheskih protsessov. LAP LAMBERT Academic Publishing, 160.
Loskutov, A. Yu., Zhuravlev, D. I., Kotliarov, O. L. (2003). Primenenie metoda lokal'noy approksimatsii dlia prognoza iekonomicheskih pokazateley. Voprosy analiza i upravleniia riskom, T. 1, № 1, 21-31.
Chistiakova, A., Shamsha, B. (2014). Information technology of forecasting non-stationary time-series data using singular spectrum analysis. Eastern-European Journal Of Enterprise Technologies, 2(4(68)), 24-30. Available: http://journals.uran.ua/eejet/article/view/22158.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 Анна Александровна Чистякова
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.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.
