چکیده :
Kernel ridge regression is a technique to perform ridge regression with a potentially infinite
number of nonlinear transformations of the independent variables as regressors. This
method is gaining popularity as a data-rich nonlinear forecasting tool, which is applicable
in many different contexts. The influence of the choice of kernel and the setting of tuning
parameters on forecast accuracy is investigated. Several popular kernels are reviewed, including
polynomial kernels, the Gaussian kernel, and the Sinc kernel. The latter two kernels
are interpreted in terms of their smoothing properties, and the tuning parameters associated
to all these kernels are related to smoothness measures of the prediction function
and to the signal-to-noise ratio. Based on these interpretations, guidelines are provided 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 make them widely
applicable. Therefore, their use is recommended instead of the popular polynomial kernels
in general settings, where no information on the data-generating process is available.
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