# [R] Bug : Autocorrelation in sample drawn from stats::rnorm

hmh hugomh @ending from gmx@fr
Thu Oct 4 12:09:01 CEST 2018

```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)
}

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 using r-project.org>
Description: R statistical functions.
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

--
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Hugo Mathé-Hubert

ATER

Laboratoire Interdisciplinaire des Environnements Continentaux (LIEC)

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Université de Lorraine  -  UFR SciFA

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