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MathGroup Archive 1994

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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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