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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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-138/4.

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Date of creation: 29 Sep 2011
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Handle: RePEc:dgr:uvatin:20110138

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Web page: http://www.tinbergen.nl

Related research

Keywords: nonlinear forecasting; shrinkage estimation; kernel methods; high dimensionality;

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References

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  1. 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.
  2. Timo Teräsvirta & Dick van Dijk & Marcelo Cunha Medeiros, 2004. "Linear models, smooth transition autoregressions and neural networks for forecasting macroeconomic time series: A reexamination," Textos para discussão 485, Department of Economics PUC-Rio (Brazil).
  3. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
  4. Sydney Ludvigson & Serena Ng, 2006. "The Empirical Risk-Return Relation: a factor analysis approach," 2006 Meeting Papers 236, Society for Economic Dynamics.
  5. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836, September.
  6. Novales, Alfonso, 2005. "Comments on: "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 775-780.
  7. 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.
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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 2012-07-26 19:23:25
  2. Kernel Ridge Regression – A Toy Example
    by Clive Jones in Business Forecasting on 2014-03-01 21:10:25

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