Hybrid mathematical models and methods for forecasting related nonstationary time series

Authors

  • Виталий Николаевич Щелкалин Kharkіv National University of Radioelectronics 14, Lenina str., Kharkiv, Ukraine, 61166, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2015.37317

Keywords:

forecasting, structural identification, decomposition model, Box-Jenkins method, "Caterpillar"-SSA method

Abstract

The paper presents mathematical models for forecasting related nonstationary time series and methods for their structural identification based on the joint use of a multidimensional variant of the "Caterpillar"-SSA method and VARMAX and SARIMAX models.

In the proposed hybrid mathematical models, using formulas for L- or K-continuation of multi-dimensional variant of the "Caterpillar"-SSA method, structural and parametric identification of the transfer function, connecting the endogenous and exogenous time series is carried out. Decomposition approach to time series forecasting based on multi-dimensional variant of the "Caterpillar"-SSA method and SARIMAX models lies in decomposition of source endogenous and exogenous time series into multiple time series with a simpler structure using the multidimensional "Caterpillar"-SSA method; forecasting data of decomposition components by SARIMAX models and calculating the total forecast for each endogenous time series, combining forecasts, constructed for simplified models.

The proposed models were tested on the example of forecasting physical parameters of the natural gas consumption processes of the linear parts of the gas transportation system, and the forecasting results were compared with the results, obtained by the VARMAX models. Experimental results show the high efficiency of the proposed forecasting models for selecting suitable structural parameters in comparison with the VARMAX models.

The results lead to the conclusion that for effective forecasts, it is necessary to perform the decomposition of the studied time series and combine different models, describing both statistical and deterministic time series components, which provides better forecasting.

Author Biography

Виталий Николаевич Щелкалин, Kharkіv National University of Radioelectronics 14, Lenina str., Kharkiv, Ukraine, 61166

Assistant of Department of Applied Mathematics

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Published

2015-02-27

How to Cite

Щелкалин, В. Н. (2015). Hybrid mathematical models and methods for forecasting related nonstationary time series. Eastern-European Journal of Enterprise Technologies, 1(4(73), 42–58. https://doi.org/10.15587/1729-4061.2015.37317

Issue

Vol. 1 No. 4(73) (2015): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

Copyright (c) 2015 Віталій Миколайович Щелкалін

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