Kernel Smoothing
Kernel smoothing is a group of powerful smoothing algorithms that consists in applying a function known as the kernel to each data point in the time-series. Kernel Smoothing belongs
to the class of weighted moving averages.
This means in practice that all the points in the time-series are weighted using as weights the results of the computation of the kernel function.
Every kernel function has several properties:
All kernel values are positive or zero.
The kernel functions are normally symmetric.
Kernel function values decrease to zero from a central (maximum) value.
The kernel functions supported by IPredict’s library are the following:
| Kernel Name |
Kernel Equation |
Kernel Example Plot |
| Gaussian |
K(t) = e-λ * t2 |
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| Hilbert |
K(t) = -π / t |
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| Triangle |
K(T) = 1 - Abs(t) |
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| Epanechnicov |
K(t) = 3/4 * (1 - t2) |
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| Quartic |
K(t) = 15/16 * (1 - t2)2 |
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| Triweight |
K(t) = 35/32 * (1 - t2)3 |
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| Cosine |
K(t) = -π/4 * Cos(π/2 * t) |
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References:
Kernel Smoothing, M.P. Wand and M.C. Jones
White Noise Theory of Prediction, Filtering and Smoothing, G. Kallianpur and Rajeeva Karandikar
Wikipedia definition for Kernel
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