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Model Selection in Kernel Ridge Regression

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  • Peter Exterkate

    ()
    (Department of Economics and CREATES Aarhus University)

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 popular polynomial kernels in general settings, in which no information on the data-generating process is available.

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File URL: ftp://ftp.econ.au.dk/creates/rp/12/rp12_10.pdf
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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-10.

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Length: 22
Date of creation: 28 Feb 2012
Date of revision:
Handle: RePEc:aah:create:2012-10

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Web page: http://www.econ.au.dk/afn/

Related research

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

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References

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  1. Teräsvirta, Timo & van Dijk, Dick & Medeiros, Marcelo, 2004. "Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A re-examination," Working Paper Series in Economics and Finance 561, Stockholm School of Economics, revised 04 Nov 2004.
  2. 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.
  3. Sydney Ludvigson & Serena Ng, 2006. "The Empirical Risk-Return Relation: a factor analysis approach," 2006 Meeting Papers 236, Society for Economic Dynamics.
  4. 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.
  5. Peter Exterkate & Patrick J.F. Groenen & Christiaan Heij & Dick van Dijk, 2013. "Nonlinear Forecasting With Many Predictors Using Kernel Ridge Regression," CREATES Research Papers 2013-16, School of Economics and Management, University of Aarhus.
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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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Cited by:
  1. Peter Exterkate & Patrick J.F. Groenen & Christiaan Heij & Dick van Dijk, 2013. "Nonlinear Forecasting With Many Predictors Using Kernel Ridge Regression," CREATES Research Papers 2013-16, School of Economics and Management, University of Aarhus.

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