Annaert Jan
2018-Oct-05 07:58 UTC
[R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)
On 05/10/2018, 09:45, "R-help on behalf of hmh" <r-help-bounces at
r-project.org on behalf of hugomh at gmx.fr> wrote:
Hi,
Thanks William for this fast answer, and sorry for sending the 1st mail
to r-help instead to r-devel.
I noticed that bug while I was simulating many small random walks using
c(0,cumsum(rnorm(10))). Then the negative auto-correlation was inducing
a muchsmaller space visited by the random walks than expected if there
would be no auto-correlation in the samples.
The code I provided and you optimized was only provided to illustrated
and investigate that bug.
It is really worrying that most of the R distributions are affected by
this bug !!!!
What I did should have been one of the first check done for _*each*_
distributions by the developers of these functions !
And if as you suggested this is a "tolerated" _error_ of the
algorithm,
I do think this is a bad choice, but any way, this should have been
mentioned in the documentations of the functions !!
cheers,
hugo
This is not a bug. You have simply rediscovered the finite-sample bias in the
sample autocorrelation coefficient, known at least since
Kendall, M. G. (1954). Note on bias in the estimation of autocorrelation.
Biometrika, 41(3-4), 403-404.
The bias is approximately -1/T, with T sample size, which explains why it seems
to disappear in the larger sample sizes you consider.
Jan
hmh
2018-Oct-05 08:11 UTC
[R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)
Nope.
This IS a bug:
_*The negative auto-correlation mostly disappear when I randomize small
samples using the R function '*__*sample*__*'.*_
Please check thoroughly the code of the 1st mail I sent, there should be
no difference between the two R functions I wrote to illustrate the bug.
The two functions that should produce the same output if there would be
no bug are 'DistributionAutocorrelation_Unexpected' and
'DistributionAutocorrelation_Expected'.
_/Please take the time to compare there output!!/_
The finite-sample bias in the sample autocorrelation coefficient you
mention should affect them in the same manner. This bias is not the only
phenomenon at work, *_there is ALSO as BUG !_*
Thanks
The first mail I sent is below :
_ _ _
Hi,
I just noticed the following bug:
When we draw a random sample using the function stats::rnorm, there
should be not auto-correlation in the sample. But their is some
auto-correlation _when the sample that is drawn is small_.
I describe the problem using two functions:
DistributionAutocorrelation_Unexpected which as the wrong behavior :
_when drawing some small samples using rnorm, there is generally a
strong negative auto-correlation in the sample_.
and
DistributionAutocorrelation_Expected which illustrate the expected behavior
*Unexpected : *
DistributionAutocorrelation_Unexpected = function(SampleSize){
? Cor = NULL
? for(repetition in 1:1e5){
??? X = rnorm(SampleSize)
??? Cor[repetition] = cor(X[-1],X[-length(X)])
? }
? return(Cor)
}
par(mfrow=c(3,3))
for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){
hist(DistributionAutocorrelation_Unexpected(SampleSize_),col='grey',main=paste0('SampleSize=',SampleSize_))
; abline(v=0,col=2)
}
output:
*Expected**:*
DistributionAutocorrelation_Expected = function(SampleSize){
? Cor = NULL
? for(repetition in 1:1e5){
??? X = rnorm(SampleSize)
*??? Cor[repetition] = cor(sample(X[-1]),sample(X[-length(X)]))*
? }
? return(Cor)
}
par(mfrow=c(3,3))
for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){
hist(DistributionAutocorrelation_Expected(SampleSize_),col='grey',main=paste0('SampleSize=',SampleSize_))
; abline(v=0,col=2)
}
Some more information you might need:
packageDescription("stats")
Package: stats
Version: 3.5.1
Priority: base
Title: The R Stats Package
Author: R Core Team and contributors worldwide
Maintainer: R Core Team <R-core at r-project.org>
Description: R statistical functions.
License: Part of R 3.5.1
Imports: utils, grDevices, graphics
Suggests: MASS, Matrix, SuppDists, methods, stats4
NeedsCompilation: yes
Built: R 3.5.1; x86_64-pc-linux-gnu; 2018-07-03 02:12:37 UTC; unix
Thanks for correcting that.
fill free to ask any further information you would need.
cheers,
hugo
On 05/10/2018 09:58, Annaert Jan wrote:> On 05/10/2018, 09:45, "R-help on behalf of hmh"
<r-help-bounces at r-project.org on behalf of hugomh at gmx.fr> wrote:
>
> Hi,
>
> Thanks William for this fast answer, and sorry for sending the 1st
mail
> to r-help instead to r-devel.
>
>
> I noticed that bug while I was simulating many small random walks
using
> c(0,cumsum(rnorm(10))). Then the negative auto-correlation was
inducing
> a muchsmaller space visited by the random walks than expected if there
> would be no auto-correlation in the samples.
>
>
> The code I provided and you optimized was only provided to illustrated
> and investigate that bug.
>
>
> It is really worrying that most of the R distributions are affected by
> this bug !!!!
>
> What I did should have been one of the first check done for _*each*_
> distributions by the developers of these functions !
>
>
> And if as you suggested this is a "tolerated" _error_ of the
algorithm,
> I do think this is a bad choice, but any way, this should have been
> mentioned in the documentations of the functions !!
>
>
> cheers,
>
> hugo
>
> This is not a bug. You have simply rediscovered the finite-sample bias in
the sample autocorrelation coefficient, known at least since
> Kendall, M. G. (1954). Note on bias in the estimation of autocorrelation.
Biometrika, 41(3-4), 403-404.
>
> The bias is approximately -1/T, with T sample size, which explains why it
seems to disappear in the larger sample sizes you consider.
>
> Jan
>
--
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Thoughts appear from doubts and die in convictions. Therefore, doubts
are an indication of strength and convictions an indication of weakness.
Yet, most people believe the opposite.
Annaert Jan
2018-Oct-05 08:28 UTC
[R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)
> Nope.> This IS a bug: > The negative auto-correlation mostly disappear when I randomize small samples using the R function 'sample'.> Please check thoroughly the code of the 1st mail I sent, there should be no difference between the two R functions I wrote to illustrate the bug. > The two functions that should produce the same output if there would be no bug are 'DistributionAutocorrelation_Unexpected' and 'DistributionAutocorrelation_Expected'. >Please take the time to compare there output!! >The finite-sample bias in the sample autocorrelation coefficient you mention should affect them in the same manner. This bias is not the only phenomenon at work, there is ALSO as BUG !I disagree. Take a look at your code: Cor[repetition] = cor(sample(X[-1]),sample(X[-length(X)])) By sampling the two series in the correlation function, you discard any time series structure; you are no longer estimating a serial correlation coefficient, but just a correlation (which in this case is unbiased). Try out the following: Xs <- sample(X) Cor[repetition] = cor(Xs[-1]),(Xs[-length(Xs)])) The bias should reappear. Jan -------------- next part -------------- A non-text attachment was scrubbed... Name: cclhgmpcmhoinmca.png Type: image/png Size: 76147 bytes Desc: cclhgmpcmhoinmca.png URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20181005/1c25e7f4/attachment-0004.png> -------------- next part -------------- A non-text attachment was scrubbed... Name: adeokhkijhbomjkp.png Type: image/png Size: 75264 bytes Desc: adeokhkijhbomjkp.png URL: <https://stat.ethz.ch/pipermail/r-help/attachments/20181005/1c25e7f4/attachment-0005.png>