Dear R-users,
I have been using R and its core-packages with great satisfaction now for many
years, and have recently started using the "ccf" function (part of the "stats"
package version 2.16.0), about which I have a question.
The "ccf"-algorithm for calculating the cross-correlation between two time
series always calculates the mean and standard deviation per time series
beforehand, thereby using a constant value for these irrespective of any
time-lag. Another piece of statistical software that I'm using, a toolbox in
Matlab, does this in a fundamentally different way. It first "chops off" the
parts of the time-series that do not overlap when a time-lag has been
introduced, and then calculates a new mean and standard deviation to be used
for further calculations. This latter method has the advantage of always
theoretically still being able to obtain a cross-correlation of 1 (or -1),
whereas the "ccf"-method of R seems to introduce zeros at the non-overlapping
parts of the time-series, thereby preventing this possibility and producing
very different results. Take for instance the two time series: a = {1,3,2} and
b = {3,2,1}. The query "ccf(a,b)" produces the output {-0.5, -0.5, 0.5}, but I
would t!
hink that
a time-lag of -1 should produce a cross-correlation here of 1, since the two
time series will overlap with identical parts {3,2}.
I have attached clean implementations (removing all dependencies) of how the R
algorithm seems to calculate cross-correlations with time-lag (it produces
identical results to "ccf"), and how this other method (in Matlab) calculates
it (with newly calculated means and standard deviation for each time-lag).
Could someone be so kind as to explain to me why the "ccf"-algorithm has this
specific implementation that seems to, at least for specific situations,
produce results with artifacts? It is very likely that the R-implementation, as
opposed to the alternative algorithm described above and in the attachment, has
a very good statistical explanation, but one that unfortunately is not dawning
on me.
Sincerely,
Tim Dorscheidt
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