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

Annaert Jan j@n@@nn@ert @ending from u@ntwerpen@be
Fri Oct 5 10:28:05 CEST 2018

> 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.


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