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Ich habe eine Zeitreihe zBK Bandpaßfilters R und Gibbs-Phänomen
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1922 -0.25108773 -0.27732553 -0.29703807 -0.30274000 -0.30323653 -0.28441682 -0.24106527 -0.18705071 -0.17440826 -0.17291725 -0.19116734 -0.21678948
1923 -0.24487998 -0.26658925 -0.28613991 -0.29674346 -0.29335742 -0.28325761 -0.23326680 -0.18697904 -0.18443807 -0.18144226 -0.18190910 -0.21574376
1924 -0.24465806 -0.27349425 -0.29925888 -0.30386766 -0.30250722 -0.27464960 -0.23390958 -0.19300616 -0.17910621 -0.17869576 -0.19611839 -0.20447324
1925 -0.25326812 -0.27344637 -0.29352971 -0.30947682 -0.30872025 -0.27604449 -0.24065208 -0.19676031 -0.17172229 -0.18484153 -0.19542607 -0.21841577
1926 -0.25214568 -0.27450911 -0.29438956 -0.30392114 -0.30619846 -0.29089168 -0.24829621 -0.20204202 -0.18621514 -0.18808172 -0.19708748 -0.22629595
1927 -0.25107357 -0.27204514 -0.29494695 -0.30751442 -0.30800040 -0.28569694 -0.24655626 -0.19547608 -0.19018517 -0.18866641 -0.20132372 -0.22084811
1928 -0.24733214 -0.27490388 -0.28780308 -0.30407576 -0.30857301 -0.28629658 -0.23872777 -0.19590465 -0.18437917 -0.18274289 -0.19936931 -0.22368973
1929 -0.25531870 -0.27264628 -0.29418746 -0.30385231 -0.31022219 -0.27931003 -0.23404912 -0.19538227 -0.17226595 -0.18465123 -0.19072933 -0.22043396
1930 -0.24735028 -0.27386782 -0.29193707 -0.29925459 -0.30039372 -0.28014958 -0.23551136 -0.19511701 -0.18006660 -0.18282789 -0.20113355 -0.22095253
1931 -0.24903438 -0.27439043 -0.29219506 -0.30312159 -0.30557600 -0.28180333 -0.22676008 -0.19048014 -0.18982644 -0.18459638 -0.19550196 -0.22127202
1932 -0.25870503 -0.27650825 -0.28521052 -0.30685609 -0.30896898 -0.28378619 -0.23614859 -0.18945699 -0.17575919 -0.17820312 -0.19620912 -0.21774873
1933 -0.24187599 -0.25575287 -0.28325644 -0.29554461 -0.29018996 -0.27040369 -0.23514812 -0.19935749 -0.18732198 -0.18606057 -0.19327237 -0.22321366
1934 -0.24793807 -0.26986056 -0.29217378 -0.30479126 -0.30199154 -0.27574924 -0.24097380 -0.18560708 -0.18643606 -0.18501770 -0.19375478 -0.22418002
1935 -0.25587642 -0.27805131 -0.29239104 -0.30784907 -0.30459449 -0.28216514 -0.23839965 -0.20137460 -0.18619998 -0.18328896 -0.20121286 -0.22869388
1936 -0.25322320 -0.28025116 -0.29713940 -0.30800346 -0.31177201 -0.28473251 -0.23552472 -0.20313945 -0.18251793 -0.18383941 -0.20554430 -0.23061875
1937 -0.26268769 -0.28529769 -0.30230641 -0.31107806 -0.30183547 -0.28324508 -0.23840574 -0.19862786 -0.19297314 -0.19392849 -0.19603212 -0.22877177
1938 -0.25445601 -0.28160871 -0.29837676 -0.29879519 -0.30328832 -0.28288226 -0.23577573 -0.19521124 -0.18393512 -0.19039895 -0.20537533 -0.21924241
1939 -0.25180969 -0.28199995 -0.29601764 -0.30147945 -0.30372884 -0.27837795 -0.23720063 -0.19929773 -0.18770674 -0.19341142 -0.20753282 -0.22484697
1940 -0.15145157 -0.16596690 -0.17572643 -0.18225920 -0.18823836 -0.17504012 -0.16019626 -0.12920340 -0.12369614 -0.12024704 -0.12891992 -0.14234080
1941 -0.10045275 -0.11095497 -0.11585389 -0.11932455 -0.11976700 -0.11653216 -0.10259231 -0.08271703 -0.07621320 -0.07184160 -0.07284514 -0.07385666
1942 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1943 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1944 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1945 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1946 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1947 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1948 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1949 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1950 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1951 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1952 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1953 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1954 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1955 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1956 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1957 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1958 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1959 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1960 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
1961 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
und ich mag einen banpassfilter bei 9,7 Monaten und 16 Monaten durchzuführen. Ich habe die bkfilter (package MFilter)
jedoch nach 1942 angewendet, wenn z Null ist der Filter zeigt noch einige kleine Zyklen. In einem früheren Schritt (Band-pass filter in R: weird behaviour at the end of time series) wurde mir vorgeschlagen, dass dieses Verhalten durch das Gibbs-Phänomen verursacht werden könnte. Ich habe korrigiert dann die bkfunction wie hier beschrieben http://www.gla.ac.uk/media/media_219052_en.pdf
### Baxter-King filter
modbkfilter <- function(x,pl=NULL,pu=NULL,nfix=NULL,typeBK=c("regular","modified"),type=c("fixed"),drift=FALSE)
{
if(is.null(drift)) drift <- FALSE
xname=deparse(substitute(x))
type = match.arg(type)
if(is.null(type)) type <- "fixed"
if(is.ts(x))
freq=frequency(x)
else
freq=1
if(is.null(pl))
{
if(freq > 1)
pl=trunc(freq*1.5)
else
pl=2
}
if(is.null(pu))
pu=trunc(freq*8)
b = 2*pi/pl
a = 2*pi/pu
n = length(x)
if(n<5)
warning("# of observations in Baxter-King filter < 5")
if(pu<=pl)
stop("pu must be larger than pl")
if(pl<2)
{
warning("in Baxter-King kfilter, pl less than 2 , reset to 2")
pl = 2
}
if(is.null(nfix))
nfix = freq*3
if(nfix>=n/2)
stop("fixed lag length must be < n/2")
j = 1:(2*n)
if(typeBK=="regular") B = as.matrix(c((b-a)/pi,(sin(j*b)-sin(j*a))/(j*pi)))
if(typeBK=="modified") B = as.matrix(c(
(b-a)/pi,
((sin(j*b)-sin(j*a))/(j*pi)) * (sin((2*pi*j)/(2*nfix+1))/((2*pi*j)/(2*nfix+1)))
))
AA = matrix(0,n,n)
if(type=="fixed")
{
bb = matrix(0,2*nfix+1,1)
bb[(nfix+1):(2*nfix+1)] = B[1:(nfix+1)]
bb[nfix:1] = B[2:(nfix+1)]
bb = bb-sum(bb)/(2*nfix+1)
for(i in (nfix+1):(n-nfix))
AA[i,(i-nfix):(i+nfix)] = t(bb)
}
xo = x
x = as.matrix(x)
if(drift)
x = undrift(x)
x.cycle = AA%*%as.matrix(x)
x.cycle[c(1:nfix,(n-nfix+1):n)] = NA
x.trend = x-x.cycle
if(is.ts(xo))
{
tsp.x = tsp(xo)
x.cycle=ts(x.cycle,star=tsp.x[1],frequency=tsp.x[3])
x.trend=ts(x.trend,star=tsp.x[1],frequency=tsp.x[3])
x=ts(x,star=tsp.x[1],frequency=tsp.x[3])
}
res <- list(cycle=x.cycle,trend=x.trend,fmatrix=AA,title="Baxter-King Filter",
xname=xname,call=as.call(match.call()),
type=type,pl=pl,pu=pu,nfix=nfix,method="bkfilter",x=x)
return(structure(res,class="mFilter"))
}
jedoch die Ergebnisse nicht viel
Jede Hilfe nicht ändert?
