[R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)

hmh hugomh @end|ng |rom gmx@|r
Fri Oct 5 10:11:53 CEST 2018


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 

_/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 !_*


The first mail I sent is below :

_ _ _


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_.


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)])

for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){
; abline(v=0,col=2)



DistributionAutocorrelation_Expected = function(SampleSize){
   Cor = NULL
   for(repetition in 1:1e5){
     X = rnorm(SampleSize)
*    Cor[repetition] = cor(sample(X[-1]),sample(X[-length(X)]))*

for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){
; abline(v=0,col=2)

Some more information you might need:

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 using 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.



On 05/10/2018 09:58, Annaert Jan wrote:
> On 05/10/2018, 09:45, "R-help on behalf of hmh" <r-help-bounces using r-project.org on behalf of hugomh using 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

- no title specified

Hugo Mathé-Hubert


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