Determining a Piecewise Linear Trend of a Nonstationary Time Series Based on Intelligent Data Analysis. II. Machine Experiments and Solution of the Practical Problem
The article describes the results of the approbation of the method of constructing a piecewise linear trend, which can have breaks at the switching points as well as be continuous at these points, i.e., represent a linear spline. An example of applying the method for constructing a linear switching...
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| Published in | Cybernetics and systems analysis Vol. 60; no. 2; pp. 220 - 233 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.03.2024
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1060-0396 1573-8337 |
| DOI | 10.1007/s10559-024-00663-w |
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| Abstract | The article describes the results of the approbation of the method of constructing a piecewise linear trend, which can have breaks at the switching points as well as be continuous at these points, i.e., represent a linear spline. An example of applying the method for constructing a linear switching regression, which has two independent variables with a trend, is considered. The problems of spline approximation of the time series of logarithms of the number of people infected with COVID-19 in Ukraine are solved. |
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| AbstractList | The article describes the results of the approbation of the method of constructing a piecewise linear trend, which can have breaks at the switching points as well as be continuous at these points, i.e., represent a linear spline. An example of applying the method for constructing a linear switching regression, which has two independent variables with a trend, is considered. The problems of spline approximation of the time series of logarithms of the number of people infected with COVID-19 in Ukraine are solved. The article describes the results of the approbation of the method of constructing a piecewise linear trend, which can have breaks at the switching points as well as be continuous at these points, i.e., represent a linear spline. An example of applying the method for constructing a linear switching regression, which has two independent variables with a trend, is considered. The problems of spline approximation of the time series of logarithms of the number of people infected with COVID-19 in Ukraine are solved. Keywords: trend, regression, switching point, spline, real-time calculation. |
| Audience | Academic |
| Author | Korkhin, A. S. Knopov, P. S. |
| Author_xml | – sequence: 1 givenname: P. S. surname: Knopov fullname: Knopov, P. S. email: knopov1@yahoo.com organization: V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine – sequence: 2 givenname: A. S. surname: Korkhin fullname: Korkhin, A. S. organization: Prydniprovska State Academy of Civil Engineering and Architecture |
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| Cites_doi | 10.1007/s40435-023-01135-3 10.1007/s10559-018-0045-9 10.1007/s10559-020-00314-w 10.1007/s11238-005-3217-9 10.1111/jtsa.12248 10.1007/BF02667038 10.1007/s10559-020-00258-1 10.1007/s10559-018-0071-7 10.1007/s10559-024-00646-x 10.1007/978-1-4614-0574-0 |
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| References | PerronPZortaEEstimation and inference of linear trend slope ratios with an application to global temperature dataJ. of Time Series Analysis20173856306673689440 GolodnikovANKnopovPSPepelyaevVAEstimation of reliability parameters under incomplete primary informationTheory and Decision2004574331344220134810.1007/s11238-005-3217-9 KnopovPSKorkhinASDetermining a piecewise linear trend of a nonstationary time series based on intelligent data analysis. I. Description and substantiation of the methodCybern. Syst. Analysis2024601505910.1007/s10559-024-00646-x KorkhinASAn approximate method of constructing a switching regression with unknown switch pointsCybern. Syst. Analysis2020563426438411286010.1007/s10559-020-00258-1 KnopovPSKorkhinASStatistical analysis of the dynamics of coronavirus cases using stepwise switching regressionCybern. Syst. Analysis202056694395210.1007/s10559-020-00314-w P. S. Knopov and A. S. Korkhin, Regression Analysis Under A Priori Parameter Restrictions, Ser. Springer Optimization and Its Applications, Vol. 54, Springer, New York (2011). https://doi.org/10.1007/978-1-4614-0574-0. NorkinVIGaivoronskiAAZaslavskyVAKnopovPSModels of the optimal resource allocation for the critical infrastructure protectionCybern. Syst. Analysis201854569670610.1007/s10559-018-0071-7 KnopovPSKorkhinASDynamic models of epidemiology in discrete time taking into account processes with lagInt. J. Dynam. Control20231121932214463150410.1007/s40435-023-01135-3 KorkhinASConstructing a switching regression with unknown switching pointsCybern. Syst. Analysis2018543443455379444710.1007/s10559-018-0045-9 KorkhinASParameter estimation accuracy for nonlinear regression with nonlinear constraintsCybern. Syst. Analysis1998345663672171198710.1007/BF02667038 PS Knopov (663_CR7) 2020; 56 AN Golodnikov (663_CR9) 2004; 57 PS Knopov (663_CR3) 2024; 60 P Perron (663_CR4) 2017; 38 663_CR1 AS Korkhin (663_CR2) 1998; 34 AS Korkhin (663_CR5) 2018; 54 VI Norkin (663_CR10) 2018; 54 AS Korkhin (663_CR6) 2020; 56 PS Knopov (663_CR8) 2023; 11 |
| References_xml | – reference: NorkinVIGaivoronskiAAZaslavskyVAKnopovPSModels of the optimal resource allocation for the critical infrastructure protectionCybern. Syst. Analysis201854569670610.1007/s10559-018-0071-7 – reference: PerronPZortaEEstimation and inference of linear trend slope ratios with an application to global temperature dataJ. of Time Series Analysis20173856306673689440 – reference: KorkhinASConstructing a switching regression with unknown switching pointsCybern. Syst. Analysis2018543443455379444710.1007/s10559-018-0045-9 – reference: KnopovPSKorkhinASDetermining a piecewise linear trend of a nonstationary time series based on intelligent data analysis. I. Description and substantiation of the methodCybern. Syst. Analysis2024601505910.1007/s10559-024-00646-x – reference: KorkhinASParameter estimation accuracy for nonlinear regression with nonlinear constraintsCybern. Syst. Analysis1998345663672171198710.1007/BF02667038 – reference: P. S. Knopov and A. S. Korkhin, Regression Analysis Under A Priori Parameter Restrictions, Ser. Springer Optimization and Its Applications, Vol. 54, Springer, New York (2011). https://doi.org/10.1007/978-1-4614-0574-0. – reference: KorkhinASAn approximate method of constructing a switching regression with unknown switch pointsCybern. Syst. Analysis2020563426438411286010.1007/s10559-020-00258-1 – reference: KnopovPSKorkhinASDynamic models of epidemiology in discrete time taking into account processes with lagInt. J. Dynam. Control20231121932214463150410.1007/s40435-023-01135-3 – reference: GolodnikovANKnopovPSPepelyaevVAEstimation of reliability parameters under incomplete primary informationTheory and Decision2004574331344220134810.1007/s11238-005-3217-9 – reference: KnopovPSKorkhinASStatistical analysis of the dynamics of coronavirus cases using stepwise switching regressionCybern. Syst. Analysis202056694395210.1007/s10559-020-00314-w – volume: 11 start-page: 2193 year: 2023 ident: 663_CR8 publication-title: Int. J. Dynam. Control doi: 10.1007/s40435-023-01135-3 – volume: 54 start-page: 443 issue: 3 year: 2018 ident: 663_CR5 publication-title: Cybern. Syst. Analysis doi: 10.1007/s10559-018-0045-9 – volume: 56 start-page: 943 issue: 6 year: 2020 ident: 663_CR7 publication-title: Cybern. Syst. Analysis doi: 10.1007/s10559-020-00314-w – volume: 57 start-page: 331 issue: 4 year: 2004 ident: 663_CR9 publication-title: Theory and Decision doi: 10.1007/s11238-005-3217-9 – volume: 38 start-page: 630 issue: 5 year: 2017 ident: 663_CR4 publication-title: J. of Time Series Analysis doi: 10.1111/jtsa.12248 – volume: 34 start-page: 663 issue: 5 year: 1998 ident: 663_CR2 publication-title: Cybern. Syst. Analysis doi: 10.1007/BF02667038 – volume: 56 start-page: 426 issue: 3 year: 2020 ident: 663_CR6 publication-title: Cybern. Syst. Analysis doi: 10.1007/s10559-020-00258-1 – volume: 54 start-page: 696 issue: 5 year: 2018 ident: 663_CR10 publication-title: Cybern. Syst. Analysis doi: 10.1007/s10559-018-0071-7 – volume: 60 start-page: 50 issue: 1 year: 2024 ident: 663_CR3 publication-title: Cybern. Syst. Analysis doi: 10.1007/s10559-024-00646-x – ident: 663_CR1 doi: 10.1007/978-1-4614-0574-0 |
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| SubjectTerms | Artificial Intelligence Control COVID-19 Data analysis Epidemiology Independent variables Mathematics Mathematics and Statistics Processor Architectures Software Engineering/Programming and Operating Systems Splines Switching Systems Theory Time series |
| Title | Determining a Piecewise Linear Trend of a Nonstationary Time Series Based on Intelligent Data Analysis. II. Machine Experiments and Solution of the Practical Problem |
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