DOI: https://doi.org/10.15588/10.15588/1607-3274-2019-2-9

A COMBINED APPROACH TO MODELING NONSTATIONARY HETEROSCEDASTIC PROCESSES

O. L. Tymoshchuk, V. H. Huskova, P. I. Bidyuk

Abstract


Context. Nonlinear nonstationary processes are observed today in various fields of studies: economy, finances, ecology, demography
etc. Very often special approaches are required for model development and forecasts estimation for the processes mentioned.
The modeling methodologies have to take into consideration possible uncertainties that are encountered during data processing and
model structure and parameter estimation.
Objective. To develop a modified methodology for constructing models for nonlinear processes that allows for achieving high
quality of forecasts. More specifically heteroscedastic processes are considered that create a wide class of nonlinear nonstationary
processes and are considered in many areas of research.
Method. To reach the aim of the study mentioned the following methods are used: systemic approach to model building and
forecasting, modified methodology for modeling nonlinear processes, methods for identification and taking into consideration possible
uncertainties. To cope with the structural uncertainties following techniques: refinement of model order applying recurrent adaptive
approach to modeling and automatic search for the “best” structure using complex statistical criteria; adaptive estimation of input
delay time, and the type of data distribution with its parameters; describing detected nonlinearities with alternative analytical forms
with subsequent estimation of the forecasts generated.
Results. The proposed modified methodology for modeling nonlinear nonstationary processes, adaptation scheme for model
building, new model structures proposed. As a result of performing computational experiments, it was found that nonlinear models
constructed provide a possibility for computing high quality forecasts for the process under study and their variance.
Conclusions. Application of the modeling methodology proposed provides a possibility for structural and parametric adaptation
of the models constructed with statistical data. The models developed exhibit acceptable adequacy and quality of short-term forecasting.


Keywords


nonlinear nonstationary processes, systemic approach to modeling, structural and parametric adaptation, combined models, uncertainties in modeling and forecasting.

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References


Bidyuk P., Prosyankina-Zharova T., Terentiev O. Modeling nonlinear nonstationary processes in economy and finances, Advances in Intelligent Systems and Computing (Springer), 2018, Vol. 754, pp. 735–745. DOI: 10.1007/978-3-319-91008-6_72

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Bidyuk P. I., Тrofymchuk O.M., Kozhukhivska O. A. Probabilistic and statistical uncertainty processing using decision support systems, Visnyk of Lviv Polytechnic National University, 2015, No. 826, pp. 237–248.

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Hansen B.E. Econometrics. University of Wisconsin, 2017, 427 p. DOI: 10.1080/00220485.2017.1320610

Bidyuk P. I., Dovgij S. O., Trofymchuk O. M. DSS based on statistical and probabilistic procedures. Kyiv, Logos, 2014, 420 p.


GOST Style Citations


1. Modeling nonlinear nonstationary processes in economy and finances / [P. Bidyuk, T. Prosyankina-Zharova, O. Terentiev] // Advances in Intelligent Systems and Computing (Springer). – 2018. – Vol. 754. – P. 735–745. DOI: 10.1007/978-3-319-91008-6_72
2. De Gooijer J. G. Elements of nonlinear time series analysis and forecasting / J. G. De Gooijer. – Cham (Switzerland): Springer, 2017. – 618 p. DOI:10.1007/978-3-319-43252-6
3. Tsay R.S. Analysis of financial time series / R. S. Tsay. – New York : John Wiley & Sons, Inc., 2010. – 715 p. DOI: 10.2307/4128199
4. Time series forecasting for nonlinear and nonstationary process: a review and comparative study / [Ch. Cheng, Sa-Ngasoongsong, O. F. Beyka et al.] // IIE Transactions. – 2016. – Vol. 47. – P. 1053–1071. DOI: 10.1080/0740817X.2014.999180
5. Xekalaki E. ARCH models for financial applications / E. Xekalaki, S. Degiannakis. – Chichester : John Wiley & Sons Ltd., 2010. – 520 p. DOI:10.1002/9780470688014
6. Chen F. Y. A Comparative study of VaR estimation for structured products / F. Y. Chen // Economics Research International. – 2010, Article ID 838469. – P. 1–16. DOI: 10.1155/2010/838469
7. Diebold F. X. Comparing predicting accuracy / F. X. Diebold, R.S. Mariano // Journal of Business and Economic Statistics. – 1995. – Vol. 13. – P. 253 – 263. DOI: 10.1080/07350015.1995.10524599
8. Diebold F. X. Elements of forecasting / F. X. Diebold. – Ohio: Thomson South-Western, 2007. – 458 p. DOI:10.1016/j.ijforecast.2008.05.004
9. Bidyuk P. I. Probabilistic and statistical uncertainty processing using decision support systems / P. I. Bidyuk, O. M. Тrofymchuk, O. A. Kozhukhivska // Visnyk of Lviv Polytechnic National University. – 2015. – No. 826. – P. 237–248.
10. Diebold F. X. Forecasting in economics, business, finance and beyond / F. X. Diebold. – Pennsylvania : University of Pennsylvania, 2015. – 607 p.
11. Hansen B. E. Econometrics / B. E. Hansen. – University of Wisconsin, 2017. – 427 p. DOI: 10.1080/00220485.2017.1320610
12. Bidyuk P. I. DSS based on statistical and probabilistic procedures / P. I. Bidyuk, S. O. Dovgij, O. M. Trofymchuk. – Kyiv : Logos, 2014. – 420 p.







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