Autocorrelation and Random Numbers

• To: mathgroup at yoda.physics.unc.edu
• Subject: Autocorrelation and Random Numbers
• From: Richard L. Bowman <r.l.bowman at cescc.bridgewater.edu>
• Date: 03 Mar 94 21:28:36 EST

```I have been using Mathematica to investigate a new random number generator
function.  From the book _Numerical Recipes_, I got the idea of checking the
correlation between a generated random number and the previously produced
numbers by calculating the autocorrelation function such as done below.

In[5]:=
correl = Chop[
InverseFourier[Fourier[ran] Conjugate[Fourier[ran]]]]

Out[5]=
{1.38498, 1.05689, 1.01594, 0.96806, 0.966857,
0.929865, 0.885922, 0.882394, 0.775191, 0.818924,
0.771204, 0.828671, 0.745905, 0.781081, 0.769665,
(75 terms removed)
0.828671, 0.771204, 0.818924, 0.775191, 0.882394,
0.885922, 0.929865, 0.966857, 0.96806, 1.01594,
1.05689}

The problem is that these numbers cannot be correct since some are larger
than 1.  What have I done wrong?  How can I interpret the autocorrelation
results when I do get them?  What are some good references on correlations?
-----------------------------------------------------------------------
Richard L. Bowman
Dept. of Physics, Bridgewater College, Bridgewater, VA  22812
<r.l.bowman at bridgewater.edu>                     703-828-2501
-----------------------------------------------------------------------

```

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