kernels: Kernel function.

In quantspec: Quantile-Based Spectral Analysis of Time Series

Description

Implementations of kernel functions

Usage

W0(x)

W1(x)

W2(x)

W3(x)

WDaniell(x, a = (pi/2))

WParzen(u)

Arguments

x	real-valued argument to the function; can be a vector
a	real number between 0 and pi
u	real number

Details

Daniell kernel function W0:

1/(2pi) I{|x|<=pi}.

Epanechnikov kernel W1 (i. e., variance minimizing kernel function of order 2):

3/(4pi) (1-x/pi)^2 I{|x|<=pi}.

Variance minimizing kernel function W2 of order 4:

(15/(32 pi) (7 (x/pi)^4 - 10 (x/pi)^2 + 3) I{|x|<=pi}.

Variance minimizing kernel function W3 of order 6:

(35/(256 pi) (-99(x/pi)^6 + 189(x/pi)^4 - 105(x/pi)^2+15) I{|x|<=pi}.

Kernel yield by convolution of two Daniell kernels:

\frac{1}{π+a} \Big(1-\frac{|x|-a}{π-a} I\{a ≤q |x| ≤q π\}\Big).

Parzen Window for lagEstimators

Examples

plot(x=seq(-8,8,0.05), y=W0(seq(-8,8,0.05)), type="l")
plot(x=seq(-8,8,0.05), y=W1(seq(-8,8,0.05)), type="l")
plot(x=seq(-8,8,0.05), y=W2(seq(-8,8,0.05)), type="l")
plot(x=seq(-8,8,0.05), y=W3(seq(-8,8,0.05)), type="l")
plot(x=seq(-pi,pi,0.05), y=WDaniell(seq(-pi,pi,0.05),a=(pi/2)), type="l")
plot(x=seq(-2,2,0.05),y=WParzen(seq(-2,2,0.05)),type = "l")

quantspec documentation built on July 15, 2020, 1:07 a.m.