Model Selection in Kernel Ridge Regression
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.
|Date of creation:||28 Feb 2012|
|Date of revision:|
|Contact details of provider:|| Web page: http://www.econ.au.dk/afn/|
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- 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.
- 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.
- 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, Department of Economics and Business Economics, Aarhus University.
- Marcelo C. Medeiros & Timo Terasvirta & Gianluigi Rech, 2002.
"Building Neural Network Models for Time Series: A Statistical Approach,"
Textos para discussão
461, Department of Economics PUC-Rio (Brazil).
- 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.
- Medeiros, Marcelo C. & Teräsvirta, Timo & Rech, Gianluigi, 2002. "Building neural network models for time series: A statistical approach," SSE/EFI Working Paper Series in Economics and Finance 508, Stockholm School of Economics.
- Sydney C. Ludvigson & Serena Ng, 2005.
"The Empirical Risk-Return Relation: A Factor Analysis Approach,"
NBER Working Papers
11477, National Bureau of Economic Research, Inc.
- 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.
- Sydney Ludvigson & Serena Ng, 2006. "The Empirical Risk-Return Relation: a factor analysis approach," 2006 Meeting Papers 236, Society for Economic Dynamics.
- Teräsvirta, Timo & van Dijk, Dick & Medeiros, Marcelo, 2004.
"Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A re-examination,"
SSE/EFI Working Paper Series in Economics and Finance
561, Stockholm School of Economics, revised 04 Nov 2004.
- 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.
- 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).
- 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.
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