Dear listers,
I am working on a time series but find that for a given non-zero time
lag correlations obtained by ccf and cor are different.
x <- c(0.85472102802704641, 1.6008990694641689, 2.5019632258894835,
2.514654801253164, 3.3359198688206368, 3.5401357138398208,
2.6304117871193538, 3.6694074965420009, 3.9125153101706776,
4.4006592535478566, 3.0208991912866829, 2.959090589344433,
3.8434635568566056, 2.1683644330520457, 2.3060571563512973,
1.4680350663043942, 2.0346918622459054, 2.3674524446877538)
y <- c(2.3085729270534765, 2.0809088217491416, 1.6249456563631131,
1.5133386666933177, 0.66754156827555422, 0.3080839731181978,
0.52653042555599394, 0.89070463020837132, 0.71600791432232669,
0.82152341002975027, 0.22200290782700527, 0.6608410635137173,
0.90715232876618945, 0.45624062770725898, 0.35074487486980244,
1.1681750562971052, 1.6976462236079737, 0.88950230250556417)
cc<-ccf(x,y)
cc Autocorrelations of series ?X?, by lag -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
2 0.098 0.139 0.127 -0.043 -0.049 0.069 -0.237 -0.471 -0.668 -0.595
-0.269 -0.076 3 4 5 6 7 8 9 -0.004 0.123 0.272 0.283 0.401 0.435 0.454
cor(x,y) [1] -0.5948694
So far so good, but when I lag one of the series, I cannot find the same
correlation as with ccf
... where I expect -0.668 based on ccf
Can anyone explain why ?
The difference is explained by cff() seeing the complete data on x and
y and calculating the sample means only once, which are then used in
the calculations for each lag. cor() sees only the data you pass down,
so calculates different estimates for the means of the two sequences.
To illustrate:
[...first execute your code...]
R> xx <- x-mean(x)
R> yy <- y-mean(y)
R> n <- length(x)
R> vx <- sum(xx^2)/n
R> vy <- sum(yy^2)/n
R> (c0 <- sum(xx*yy)/n/sqrt(vx*vy))
[1] -0.5948694
R> xx <- x[1:(length(x)-1)] - mean(x)
R> yy <- y[2:length(y)] - mean(y)
R> (c1 <- sum(xx*yy)/n/sqrt(vx*vy))
[1] -0.6676418
The help page of cff() points to MASS, 4ed, the more specific reference
is p 389ff. :)
Cheers,
Berwin