Description Usage Arguments Details References See Also Examples
Kolmogorov-Zurbenko Spline
1 |
y |
data |
m |
smooth |
k |
The number of iterations for applying the KZFT |
t |
An indexing set |
Kolmogorov-Zurbenko Spline is essentially the Kolmogorov-Zurbenko Fourier Transform at the zero frequency.
I. G. Zurbenko, The spectral Analysis of Time Series. North-Holland, 1986.
I. G. Zurbenko, P. S. Porter, Construction of high-resolution wavelets, Signal Processing 65: 315-327, 1998.
R. H. Shumway, D. S. Stoffer, Time Series Analysis and Its Applications: With R Examples, Springer, 2006.
Derek Cyr and Igor Zurbenko, kzs: Kolmogorov-Zurbenko Spatial Smoothing and Applications, R-Project 2008.
Derek Cyr and Igor Zurbenko, A Spatial Spline Algorithm and an Application to Climate Waves Over the United States, 2008 Joint Statistical Meetings.
kzft
,
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | n <- 1000
x <- (1:n)/n
true<-((exp(2.5*x)+sin(25*x))-1)/3
noise <- rnorm(n)
y <- true + noise
a<-kzs(y,m=60)
par(mfrow=c(2,1))
plot(y,type='l')
lines(true,col="red")
plot(a,type='l', ylim=c(-2,4))
lines(true,col="red")
par(mfrow=c(1,1))
################
# second example
################
t <- seq(from = -round(400*pi), to = round(400*pi), by = .25)
ts <- 0.5*sin(sqrt((2*pi*abs(t))/200))
signal <- ifelse(t < 0, -ts, ts)
et <- rnorm(length(t), mean = 0, sd = 1)
yt <- et + signal
b<-kzs(yt,m=400)
par(mfrow=c(2,1))
plot(yt,type='l')
lines(signal,col="red")
plot(b,type='l', ylim=c(-0.5,1))
lines(signal,col="red")
par(mfrow=c(1,1))
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