kza (version 2.03)

kzp: Kolmogorov-Zurbenko Periodogram

Description

Kolmogorov-Zurbenko periodogram and smoothing using DiRienzo-Zurbenko (DZ).

Usage

kzp(y, m=length(y), k=1, double_frequency=FALSE)
## S3 method for class 'kzp':
smooth(object, log=TRUE, smooth_level=0.05, method = "DZ")
## S3 method for class 'kzp':
nonlinearity(x)
## S3 method for class 'kzp':
variation(x)
## S3 method for class 'kzp':
summary(object, digits=getOption("digits"), top=1, ...)
## S3 method for class 'kzp':
plot(x, \dots)
Rkzp(y, m=NULL, k=3, double_frequency=FALSE)

Arguments

y

The raw data.

m

The width of filtering window

k

The number of iterations for the KZFT

double_frequency

The return vector is half the width of the filtering window, setting this to true will give the second half.

object

Output from kzp function.

log

Use logarithm values for smoothing.

smooth_level

Percentage of smoothness to apply.

method

Method used for smoothing; choices are "DZ" or "NZ".

digits

precision of output.

top

list top values

...

Other parameters.

x

periodogram

Details

The Kolmogorov-Zurbenko Periodogram is an estimate of the spectral density using the Kolmogorov-Zurbenko Fourier Transform (KZFT).

References

I. G. Zurbenko, 1986: The spectral Analysis of Time Series. North-Holland, 248 pp. I. G. Zurbenko, P. S. Porter, Construction of high-resolution wavelets, Signal Processing 65: 315-327, 1998. A. G. DiRienzo, I. G. Zurbenko, Semi-adaptive nonparametric spectral estimation, Journal of Computational and Graphical Statistics 8(1): 41-59, 1998. R. Neagu, I. G. Zurbenko, Algorithm for adaptively smoothing the log-periodgram, Journal of the Franklin Institute 340: 103-123, 2003. Wei Yang and Igor Zurbenko, kzft: Kolmogorov-Zurbenko Fourier Transform and Applications, R-Project 2007.

See Also

kzft, kztp,

Examples

t<-1:6000
f1<-0.03
f2<-0.04
noise<-15*rnorm(length(t))
amp=1.5
s<-amp*sin(2*pi*f1*t)+amp*sin(2*pi*f2*t)
system.time(a<-kzp(s+noise,500,k=3))
b<-smooth.kzp(a, smooth_level=0.08)
par(mfrow=c(3,1))
plot(periodogram(s+noise),type='l')
plot(a)
plot(b)
par(mfrow=c(1,1))

# signal/noise
signal<-kzft(s+noise,m=500,k=3,dim=1)
print(paste("signal-to-noise ratio = ", round(sqrt(var(2*Re(signal))/var(s+noise)),4) ))

summary(a, digits=2, top=2)