Question

我有时间序列z

          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

我希望在9.7个月和16个月时执行banpassfilter。我已经应用了bkfilter（包mfilter）

然而，在1942年z为零后，滤波器仍显示一些小周期。在前一个步骤（Band-pass filter in R: weird behaviour at the end of time series）中，有人向我建议这种行为可能是由吉布斯现象引起的。然后我更正了这里描述的bkfunction 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"))
}

但结果并没有太大变化

任何帮助？

Answer 1

本文中的方程式三：

除数为(2K + 1)，但您使用了(2*nfix + 1)，自j <= 1:(2*n)以来，为什么代码中没有K <= 2*n或(2*2*n + 1)？ nfix与我看到的2*n不等。

RK和Gibbs现象中的BK带通滤波器

1 个答案: