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-c...@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-boun...@r-project.org on
behalf of hug...@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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Hugo Mathé-Hubert
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