KernelFunctions is a Pine Script v5 library that exports kernel weight functions for Nadaraya-Watson style estimation. It calculates a Rational Quadratic kernel, a Gaussian kernel based on a radial basis function, and a periodic kernel that models repeating be
Library · Pine Script v5 · Library
MathStatisticsKernelFunctions
MathStatisticsKernelFunctions is a Pine Script utility library providing statistical kernel weighting functions, including uniform, triangular, Epanechnikov, quartic, triweight, and tricubic kernels.
GitHub stars261on the repository
Pine versionv5runs as is
Lines of code197
Settings2inputs
LicenceNone statedfile: MPL-2.0
Last update4 years ago13 Nov 2021
Add It to Your TradingView Chart
- 1Copy the scriptPress Copy script above, or the copy button on the code below.
- 2Open the Pine EditorOpen a TradingView chart and choose Pine Editor at the bottom of the screen.
- 3Paste over the templateCreate a new library, select all of the template text and paste. Press Save and give it a name.
- 4Publish or import itA library draws nothing. Publish it from the editor, then import its functions in your own scripts.
Source Code
197 lines of Pine Script v5 from beta/libs/Math/Statistics/MathStatisticsKernelFunctions.pinescript, published under MPL-2.0 (file header). Keep the author's credit and licence lines when you reuse it.
// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © RicardoSantos
//@version=5
// @description TODO: add library description here
library(title='MathStatisticsKernelFunctions')
// reference:
// list: https://en.wikipedia.org/wiki/Kernel_%28statistics%29
//
// y+
// | ---------------------------------
// | | | |
// | | | |
// | | | |
// -x -----o---------------o---------------o------ +x
// -bandwidth origin (0) +bandwidth
// @function Uniform kernel.
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export uniform (float distance, float bandwidth=1.0) => //{
if math.abs(distance) > bandwidth
0.0
else
0.5
//{ usage
// b = -1 + (bar_index%100) * 0.02, plot(uniform(b, 0.9), color=color.red), plot(b, color=color.silver)
//{ remarks:
//}}}
// @function Triangular kernel.
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export triangular (float distance, float bandwidth=1.0) => //{
if math.abs(distance) > bandwidth
0.0
else
1.0 - math.abs(distance / bandwidth)
//{ usage
// b = -1.0 + (bar_index%100) * 0.02, plot(triangular(b, 0.75)), plot(b, color=color.red)
//{ remarks:
//}}}
// @function Epanechnikov kernel.
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export epanechnikov (float distance, float bandwidth=1.0) => //{
if math.abs(distance) > bandwidth
0.0
else
0.25 * (1.0 - math.pow(distance/bandwidth, 2.0))
//{ usage
// b = -1 + (bar_index%100) * 0.02, plot(epanechnikov(b, 0.9)), plot(b, color=color.red)
//{ remarks:
//}}}
// @function Quartic kernel.
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export quartic (float distance, float bandwidth=1.0) => //{
if math.abs(distance) > bandwidth
0.0
else
0.9375 * math.pow(1.0 - math.pow(distance/bandwidth, 2.0), 2.0)
//{ usage
// b = -1 + (bar_index%100) * 0.02, , plot(b, color=color.red)
//{ remarks:
//}}}
// @function Triweight kernel.
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export triweight (float distance, float bandwidth=1.0) => //{
if math.abs(distance) > bandwidth
0.0
else
(35.0 / 32.0) * math.pow(1.0 - math.pow(distance/bandwidth, 2.0), 3.0)
//{ usage
// b = -1 + (bar_index%100) * 0.02, plot(triweight(b, 0.9)), plot(b, color=color.red)
//{ remarks:
//}}}
// @function Tricubic kernel.
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export tricubic (float distance, float bandwidth=1.0) => //{
if math.abs(distance) > bandwidth
0.0
else
(70.0 / 81.0) * math.pow(1.0 - math.pow(math.abs(distance)/bandwidth, 3.0), 3.0)
//{ usage
// b = -1 + (bar_index%100) * 0.02, plot(tricubic(b, 0.9)), plot(b, color=color.red)
//{ remarks:
//}}}
// @function Gaussian kernel.
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export gaussian (float distance, float bandwidth=1.0) => //{
1.0 / math.sqrt(2.0 * math.pi) * math.pow(math.e, -0.5 * math.pow(distance / bandwidth, 2.0))
//{ usage
// b = -math.pi + (bar_index%100) * (math.pi*0.02), plot(b, color=color.red), plot(gaussian(b, 3.0)), plot(gaussian(b, 2.0), color=color.aqua), plot(gaussian(b, 1.0), color=color.yellow)
//{ remarks:
//}}}
// @function Cosine kernel.
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export cosine (float distance, float bandwidth=1.0) => //{
if math.abs(distance) > bandwidth
0.0
else
(math.pi / 4.0) * math.cos(math.pi / 2.0 * (distance / bandwidth))
//{ usage
// b = -1 + (bar_index%100) * 0.02, plot(cosine(b, 0.5)), plot(b, color=color.red)
//{ remarks:
//}}}
// @function logistic kernel.
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export logistic (float distance, float bandwidth=1.0) => //{
_d = distance / bandwidth
1.0 / (math.pow(math.e, _d) + 2.0 + math.pow(math.e, -_d))
//{ usage
// b = -1 + (bar_index%100) * 0.02, plot(logistic(b, 0.1)), plot(b, color=color.red)
//{ remarks:
//}}}
// @function Sigmoid kernel.
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export sigmoid (float distance, float bandwidth=1.0) => //{
_d = distance / bandwidth
2.0 / math.pi * (1.0 / (math.pow(math.e, _d) + math.pow(math.e, -_d)))
//{ usage
// b = -1 + (bar_index%100) * 0.02, plot(sigmoid(b, 0.1)), plot(b, color=color.red)
//{ remarks:
//}}}
// @function Kernel selection method.
// @param kernel string, kernel to select. (options="uniform", "triangle", "epanechnikov", "quartic", "triweight", "tricubic", "gaussian", "cosine", "logistic", "sigmoid")
// @param distance float, distance to kernel origin.
// @param bandwidth float, default=1.0, bandwidth limiter to weight the kernel.
// @returns float.
export select (string kernel, float distance, float bandwidth=1.0) => //{
switch (kernel)
'uniform' => uniform(distance, bandwidth)
'triangle' => triangular(distance, bandwidth)
'epanechnikov' => epanechnikov(distance, bandwidth)
'quartic' => quartic(distance, bandwidth)
'triweight' => triweight(distance, bandwidth)
'tricubic' => tricubic(distance, bandwidth)
'gaussian' => gaussian(distance, bandwidth)
'cosine' => cosine(distance, bandwidth)
'logistic' => logistic(distance, bandwidth)
'sigmoid' => sigmoid(distance, bandwidth)
=> runtime.error('MathStatisticsKernel -> select(): "kernel" invalid kernel.'), float(na)
//{ usage
// b = -1 + (bar_index%100) * 0.02, plot(select('uniform', b, 0.1)), plot(b, color=color.red)
//{ remarks:
//}}}
string choice = input.string(defval='uniform', options=["uniform", "triangle", "epanechnikov", "quartic", "triweight", "gaussian", "cosine", "logistic", "sigmoid"])
float bandwidth = input.float(0.5)
test = -1.0 + (bar_index % 100) * 0.02
plot(series=test, title='cycle', color=color.silver)
plot(series=uniform(test, bandwidth), title='uniform', color=color.red)
plot(series=triangular(test, bandwidth), title='triangle', color=color.lime)
plot(series=epanechnikov(test, bandwidth), title='epanechnikov', color=color.blue)
plot(series=quartic(test, bandwidth), title='quartic', color=color.aqua)
plot(series=triweight(test, bandwidth), title='triweight', color=color.purple)
plot(series=tricubic(test, bandwidth), title='tricubic', color=color.fuchsia)
plot(series=gaussian(test, bandwidth), title='gaussian', color=color.orange)
plot(series=cosine(test, bandwidth), title='cosine', color=color.yellow)
plot(series=logistic(test, bandwidth), title='logistic', color=color.olive)
plot(series=sigmoid(test, bandwidth), title='sigmoid', color=color.maroon)
plot(series=select(choice, test, bandwidth), title='choice', color=color.gray)
Overview
Each function takes a distance relative to the kernel origin and an optional bandwidth limit to calculate a weighted output score. When distances exceed the specified bandwidth, the kernels return zero. As a helper library, it plots nothing on the price chart and produces no direct trading signals or order executions. It serves as a mathematical calculation component for custom smoothing, regression, or machine learning tools.
- Statistical kernel functions
- Uniform, triangular, and Epanechnikov algorithms
- Quartic, triweight, and tricubic weighting
- Configurable bandwidth scaling
Details
Published by
ricardosantos79 on GitHub
Code credit
RicardoSantos, as written in the script's header
Type
Library, Pine Script v5
Draws
Library (no plots)
Markets
Any symbol
Timeframes
Any timeframe
Risk Notes
No repainting, lookahead or stacked entries were found in its code or README. That says nothing about how well it works: test it first.
Settings
The inputs you can change from the gear icon on the chart. Defaults are the author's.
| Setting | Type | Default | Variable |
|---|---|---|---|
| choice | string | uniform | choice |
| bandwidth | float | 0.5 | bandwidth |
Third-party code. ForexR did not write, test or endorse this script, and the summary above was generated automatically from its code and README. Indicators describe the past, and a strategy's backtest can look better than live trading, especially when a script repaints. Check it in the Strategy Tester and on a demo account before you rely on it.
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