[R] ccf and covariance

[Prof Brian Ripley]

On Wed, 23 Apr 2008, Bob Farmer wrote:

> Thanks to Prof. Ripley and Phil Spector for pointing out that the
> autocorrelation functions must use a "nontraditional" definition of
> the covariance, involving a denominator of n (instead of n-1) in order
> to satisfy an assumption of second-order stationarity in the
> (unbiased) covariance estimators of a time series.

Actually, they are biased.  Being a covariance sequence is the issue. 
(It's a longer explanation than I wanted or want to write out, hence my 
reference to a readily accessible source.)

> In terms of getting at the source code for the (apparently compiled)
> "R_acf", however, I've had no luck.  While
> https://svn.r-project.org/R/trunk
> seems to be able to show me the source code for otherwise obscured (in
> the R console) functions like print()
> (e.g. https://svn.r-project.org/R/trunk/src/library/base/R/print.R ),
> I can't seem to find the C code ("R_acf"?) called in this section:
> ....
> array(.C(R_acf, as.double(x), as.integer(sampleT),
>        as.integer(nser), as.integer(lag.max), as.integer(type ==
>            "correlation"), acf = double((lag.max + 1) * nser *
>            nser), NAOK = TRUE)
> ....
>
> of acf().
> For instance, in https://svn.r-project.org/R/trunk/src/library/stats/src/
> there is (seemingly) no "R_acf.C" or "stats.C" file that I would expect to see.
> I apologize in advance if this question is elementary or naive -- this
> is my first time dealing with the source code.

It is easier if you download and search the sources.  In the same way that 
ccf() is not in ccf.R, 'R_acf' is entry point 'acf' in 
src/library/stats/src/filter.c.

>
> Thanks again.
> --Bob Farmer
>
> On Wed, Apr 23, 2008 at 3:31 PM, Prof Brian Ripley
> <ripley at stats.ox.ac.uk> wrote:
>> On Wed, 23 Apr 2008, Bob Farmer wrote:
>>
>>
>>> Hi.
>>> It's my understanding that a cross-correlation function of vectors x
>>> and y at lag zero is equivalent to their correlation (or covariance,
>>> depending on how the ccf is defined).
>>>
>>
>>  The ratio of your values is
>>
>>
>>> MASS::fractions(282568.5/259021)
>>>
>>  [1] 12/11
>>
>>  ?  Do you recognize it?
>>
>>  There is an explanation in MASS4, p. 390, for example.
>>
>>
>>
>>> If this is true, could somebody please explain why I get an
>>> inconsistent result between cov() and ccf(type = "covariance"), but a
>>> consistent result between cor() and ccf(type = "correlation")?
>>> Or have I misunderstood what is a cross-correlation?
>>> (unfortunately, I can't seem to get a look at the ccf code, since I
>>> think it's buried in some C function outside of the main environment)
>>>
>>
>>  It is in the R sources, not 'buried' at all - that is what 'Open Source'
>> means. You can browse them at https://svn.r-project.org/R/trunk, or download
>> them for study.
>>
>>
>>
>>>
>>> Thanks very much.
>>> --Bob Farmer
>>> PhD candidate, Dalhousie University
>>> Halifax, NS, Canada
>>>
>>> Example:
>>> d1<-data.frame(matrix(ldeaths, nrow = 6, byrow = T))
>>> seventy_4<-as.numeric(d1[1,])
>>> seventy_5<-as.numeric(d1[2,])
>>>
>>> ccf(x=seventy_4, y=seventy_5,
>>>  plot = F, lag.max = 0, type = "covariance"
>>> )
>>> cov(seventy_4, seventy_5)  #inconsistent
>>>
>>> ccf(x=seventy_4, y=seventy_5,
>>>  plot = F, lag.max = 0, type = "correlation"
>>> )
>>> cor(seventy_4, seventy_5)  #consistent
>>>
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>>
>>
>>  --
>>  Brian D. Ripley,                  ripley at stats.ox.ac.uk
>>  Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
>>  University of Oxford,             Tel:  +44 1865 272861 (self)
>>  1 South Parks Road,                     +44 1865 272866 (PA)
>>  Oxford OX1 3TG, UK                Fax:  +44 1865 272595
>>
>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595