kza (version 4.1.0.1)

kzp: Kolmogorov-Zurbenko Periodogram

Description

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

Usage

kzp(y, m=length(y), k=1)
# S3 method for kzp
smooth(object, log=TRUE, smooth_level=0.05, method = "DZ")
# S3 method for kzp
nonlinearity(x)
# S3 method for kzp
variation(x)
# S3 method for kzp
summary(object, digits=getOption("digits"), top=1, …)
# S3 method for kzp
plot(x, …)

Arguments

y

The raw data.

m

The width of filtering window

k

The number of iterations for the KZFT

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

# NOT RUN {
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,m=500,k=3))
b<-smooth.kzp(a, smooth_level=0.01)
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)
print(paste("signal-to-noise ratio = ", round(sqrt(var(2*Re(signal))/var(s+noise)),4) ))

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