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Robust multivariate adaptive regression splines under cross-polytope uncertainty: an application in a natural gas market

Author

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  • Ayşe Özmen

    (METU
    University of Calgary)

  • Yuriy Zinchenko

    (University of Calgary)

  • Gerhard-Wilhelm Weber

    (METU
    Poznan University of Technology)

Abstract

Currently, the presence of data uncertainty and noise raises critical issues to be handled on both theoretical and computational grounds. Therefore, robustification and robust optimization have gained attention from theoretical and practical points of view for the establishment of a modeling framework in mathematical optimization to immunize solutions against diverse uncertainties. Data of both the input and output variables, underlying the problems to be addressed, are affected by the noise of different kinds, such that standard statistical models alone may not be sufficient to ensure trustworthy results due to the complexity of the model. Consequently, we propose including parametric uncertainties reflecting future scenarios in multivariate adaptive regression splines (MARS), which, in turn, show great promise for fitting nonlinear multivariate functions, where additive and interactive effects of the predictors are employed to assess the response variable. We robustify MARS through the usage of robust optimization techniques. Due to the large complexity of the underlying model in prior studies, we applied a so-called weak robustification. Now, we exploit a geometrical and combinatorial approach to allow for a more complete robustification, by formulating Robust MARS (RMARS) under Cross-Polytope Uncertainty. In this study, we use RMARS for energy data and demonstrate its superior performance through a simulation study.

Suggested Citation

  • Ayşe Özmen & Yuriy Zinchenko & Gerhard-Wilhelm Weber, 2023. "Robust multivariate adaptive regression splines under cross-polytope uncertainty: an application in a natural gas market," Annals of Operations Research, Springer, vol. 324(1), pages 1337-1367, May.
    • Handle: RePEc:spr:annopr:v:324:y:2023:i:1:d:10.1007_s10479-022-04993-w
    DOI: 10.1007/s10479-022-04993-w
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    References listed on IDEAS

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    1. Güray Kara & Ayşe Özmen & Gerhard-Wilhelm Weber, 2019. "Stability advances in robust portfolio optimization under parallelepiped uncertainty," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 241-261, March.
    2. Betül Kalaycı & Ayşe Özmen & Gerhard-Wilhelm Weber, 2020. "Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS," Annals of Operations Research, Springer, vol. 295(1), pages 183-206, December.
    3. Ayşe Özmen & Gerhard-Wilhelm Weber & Zehra Çavuşoğlu & Özlem Defterli, 2013. "The new robust conic GPLM method with an application to finance: prediction of credit default," Journal of Global Optimization, Springer, vol. 56(2), pages 233-249, June.
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    5. Magdalena Graczyk-Kucharska & Ayse Özmen & Maciej Szafrański & Gerhard Wilhelm Weber & Marek Golińśki & Małgorzata Spychała, 2020. "Knowledge accelerator by transversal competences and multivariate adaptive regression splines," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(2), pages 645-669, June.
    6. Ralf Werner, 2008. "Cascading: an adjusted exchange method for robust conic programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 179-189, June.
    7. Alper Çevik & Gerhard-Wilhelm Weber & B. Murat Eyüboğlu & Kader Karlı Oğuz, 2017. "Voxel-MARS: a method for early detection of Alzheimer’s disease by classification of structural brain MRI," Annals of Operations Research, Springer, vol. 258(1), pages 31-57, November.
    8. Bekker, Paul A, 1986. "Identification in the Linear Errors in Variables Model: Comment," Econometrica, Econometric Society, vol. 54(1), pages 215-217, January.
    9. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    10. Özmen, Ayşe & Yılmaz, Yavuz & Weber, Gerhard-Wilhelm, 2018. "Natural gas consumption forecast with MARS and CMARS models for residential users," Energy Economics, Elsevier, vol. 70(C), pages 357-381.
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    1. Phoebe Koundouri & Georgios I. Papayiannis & Electra Petracou & Athanasios Yannacopoulos, 2023. "Consensus group decision making under model uncertainty with a view towards environmental policy making," DEOS Working Papers 2305, Athens University of Economics and Business.

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