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Modelling Issues in Kernel Ridge Regression

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  • Peter Exterkate

    (Erasmus University Rotterdam)

Abstract

Kernel ridge regression is gaining popularity as a data-rich nonlinear forecasting tool, which is applicable in many different contexts. This paper investigates the influence of the choice of kernel and the setting of tuning parameters on forecast accuracy. We review several popular kernels, including polynomial kernels, the Gaussian kernel, and the Sinc kernel. We interpret the latter two kernels in terms of their smoothing properties, and we relate the tuning parameters associated to all these kernels to smoothness measures of the prediction function and to the signal-to-noise ratio. Based on these interpretations, we provide guidelines for selecting the tuning parameters from small grids using cross-validation. A Monte Carlo study confirms the practical usefulness of these rules of thumb. Finally, the flexible and smooth functional forms provided by the Gaussian and Sinc kernels makes them widely applicable, and we recommend their use instead of the pop ular polynomial kernels in general settings, in which no information on the data-generating process is available.

Suggested Citation

  • Peter Exterkate, 2011. "Modelling Issues in Kernel Ridge Regression," Tinbergen Institute Discussion Papers 11-138/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20110138
    as

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    File URL: https://papers.tinbergen.nl/11138.pdf
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    References listed on IDEAS

    as
    1. Ludvigson, Sydney C. & Ng, Serena, 2007. "The empirical risk-return relation: A factor analysis approach," Journal of Financial Economics, Elsevier, vol. 83(1), pages 171-222, January.
    2. Exterkate, Peter & Groenen, Patrick J.F. & Heij, Christiaan & van Dijk, Dick, 2016. "Nonlinear forecasting with many predictors using kernel ridge regression," International Journal of Forecasting, Elsevier, vol. 32(3), pages 736-753.
    3. Terasvirta, Timo & van Dijk, Dick & Medeiros, Marcelo C., 2005. "Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A re-examination," International Journal of Forecasting, Elsevier, vol. 21(4), pages 755-774.
    4. Sydney C. Ludvigson & Serena Ng, 2009. "Macro Factors in Bond Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(12), pages 5027-5067, December.
    5. Timo Teräsvirta & Marcelo C. Medeiros & Gianluigi Rech, 2006. "Building neural network models for time series: a statistical approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(1), pages 49-75.
    6. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    7. White, Halbert, 2006. "Approximate Nonlinear Forecasting Methods," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 9, pages 459-512, Elsevier.
    Full references (including those not matched with items on IDEAS)

    Citations

    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Kernel Ridge Regression – Example Computation I
      by Clive Jones in Business Forecasting on 2012-07-27 00:23:25
    2. Kernel Ridge Regression – A Toy Example
      by Clive Jones in Business Forecasting on 2014-03-02 03:10:25

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    More about this item

    Keywords

    nonlinear forecasting; shrinkage estimation; kernel methods; high dimensionality;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • 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

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