R help - Jan 2024 - different results between cor and ccf

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
> cor(x[1:(length(x)-1)],y[2:length(y)]) [1] -0.7903428
... where I expect -0.668 based on ccf

Can anyone explain why ?

Best,

Patrick

	[[alternative HTML version deleted]]

G'day Patrick,

On Tue, 16 Jan 2024 09:19:40 +0100
Patrick Giraudoux <patrick.giraudoux at univ-fcomte.fr> wrote:

[...]
> So far so good, but when I lag one of the series, I cannot find the
> same correlation as with ccf
> 
> > cor(x[1:(length(x)-1)],y[2:length(y)]) [1] -0.7903428  
> 
> ... 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