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Nonlinear Forecasting with Many Predictors using Kernel Ridge Regression

Author

Listed:
  • Peter Exterkate

    (Erasmus University Rotterdam)

  • Patrick J.F. Groenen

    (Erasmus University Rotterdam)

  • Christiaan Heij

    (Erasmus University Rotterdam)

  • Dick van Dijk

    (Erasmus University Rotterdam)

Abstract
This paper puts forward kernel ridge regression as an approach for forecasting with many predictors that are related nonlinearly to the target variable. In kernel ridge regression, the observed predictor variables are mapped nonlinearly into a high-dimensional space, where estimation of the predictive regression model is based on a shrinkage estimator to avoid overfitting. We extend the kernel ridge regression methodology to enable its use for economic time-series forecasting, by including lags of the dependent variable or other individual variables as predictors, as is typically desired in macroeconomic and financial applications. Monte Carlo simulations as well as an empirical application to various key measures of real economic activity confirm that kernel ridge regression can produce more accurate forecasts than traditional linear methods for dealing with many predictors based on principal component regression.

Suggested Citation

  • Peter Exterkate & Patrick J.F. Groenen & Christiaan Heij & Dick van Dijk, 2011. "Nonlinear Forecasting with Many Predictors using Kernel Ridge Regression," Tinbergen Institute Discussion Papers 11-007/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20110007
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    2. Sergei V. Akopov, 2018. "“Duty” and “Blame” in Russian Official Symbolic Representations of Sovereignty (1994-2018)," HSE Working papers WP BRP 61/PS/2018, National Research University Higher School of Economics.
    3. Alessandro Giovannelli, 2012. "Nonlinear Forecasting Using Large Datasets: Evidences on US and Euro Area Economies," CEIS Research Paper 255, Tor Vergata University, CEIS, revised 08 Nov 2012.
    4. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    5. Rajveer Jat & Daanish Padha, 2024. "Kernel Three Pass Regression Filter," Papers 2405.07292, arXiv.org, revised Jun 2024.
    6. A. Frenkel’ A. & N. Volkova N. & A. Surkov A. & E. Romanyuk I. & А. Френкель А. & Н. Волкова Н. & А. Сурков А. & Э. Романюк И., 2018. "Использование Методов Гребневой Регрессии При Объединении Прогнозов // The Application Of Ridge Regression Methods When Combining Forecasts," Финансы: теория и практика/Finance: Theory and Practice // Finance: Theory and Practice, ФГОБУВО Финансовый университет при Правительстве Российской Федерации // Financial University under The Government of Russian Federation, vol. 22(4), pages 6-17.
    7. Oslandsbotn, Andreas & Kereta, Željko & Naumova, Valeriya & Freund, Yoav & Cloninger, Alexander, 2022. "StreaMRAK a streaming multi-resolution adaptive kernel algorithm," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    8. Xu Gong & Boqiang Lin, 2018. "Structural breaks and volatility forecasting in the copper futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(3), pages 290-339, March.
    9. Wei, Yu & Liang, Chao & Li, Yan & Zhang, Xunhui & Wei, Guiwu, 2020. "Can CBOE gold and silver implied volatility help to forecast gold futures volatility in China? Evidence based on HAR and Ridge regression models," Finance Research Letters, Elsevier, vol. 35(C).
    10. Peter Exterkate, 2012. "Model Selection in Kernel Ridge Regression," CREATES Research Papers 2012-10, Department of Economics and Business Economics, Aarhus University.
    11. Hauzenberger, Niko & Huber, Florian & Klieber, Karin, 2023. "Real-time inflation forecasting using non-linear dimension reduction techniques," International Journal of Forecasting, Elsevier, vol. 39(2), pages 901-921.
    12. Tian Han & Ying Wang & Xiao Wang & Kang Chen & Huaiwu Peng & Zhenxin Gao & Lanxin Cui & Wentong Sun & Qinke Peng, 2023. "Mixed Multi-Pattern Regression for DNI Prediction in Arid Desert Areas," Sustainability, MDPI, vol. 15(17), pages 1-16, August.
    13. Markus Vogl, 2022. "Quantitative modelling frontiers: a literature review on the evolution in financial and risk modelling after the financial crisis (2008–2019)," SN Business & Economics, Springer, vol. 2(12), pages 1-69, December.
    14. Daiki Maki & Yasushi Ota, 2019. "Robust tests for ARCH in the presence of the misspecified conditional mean: A comparison of nonparametric approches," Papers 1907.12752, arXiv.org, revised Sep 2019.
    15. Kutateladze, Varlam, 2022. "The kernel trick for nonlinear factor modeling," International Journal of Forecasting, Elsevier, vol. 38(1), pages 165-177.
    16. Varlam Kutateladze, 2021. "The Kernel Trick for Nonlinear Factor Modeling," Papers 2103.01266, arXiv.org.
    17. Milan Fičura, 2019. "Forecasting Foreign Exchange Rate Movements with k-Nearest-Neighbour, Ridge Regression and Feed-Forward Neural Networks," FFA Working Papers 1.001, Prague University of Economics and Business, revised 24 Nov 2019.
    18. Cheng, Kai & Lu, Zhenzhou, 2018. "Sparse polynomial chaos expansion based on D-MORPH regression," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 17-30.
    19. Saeed Salah & Husain R. Alsamamra & Jawad H. Shoqeir, 2022. "Exploring Wind Speed for Energy Considerations in Eastern Jerusalem-Palestine Using Machine-Learning Algorithms," Energies, MDPI, vol. 15(7), pages 1-16, April.
    20. Christophe Croux & Peter Exterkate, 2011. "Sparse and Robust Factor Modelling," Tinbergen Institute Discussion Papers 11-122/4, Tinbergen Institute.
    21. Yoshiki Nakajima & Naoya Sueishi, 2022. "Forecasting the Japanese macroeconomy using high-dimensional data," The Japanese Economic Review, Springer, vol. 73(2), pages 299-324, April.
    22. Peter Exterkate, 2011. "Modelling Issues in Kernel Ridge Regression," Tinbergen Institute Discussion Papers 11-138/4, Tinbergen Institute.
    23. Wojciech Victor Fulmyk, 2023. "Nonlinear Granger Causality using Kernel Ridge Regression," Papers 2309.05107, arXiv.org.

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    More about this item

    Keywords

    High dimensionality; nonlinear forecasting; ridge regression; kernel methods;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E27 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Forecasting and Simulation: Models and Applications

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