Date: Oct 18, 2012 9:47 PM
Author: Greg Heath
Subject: Significance Levels for Correlation Functions

I standardize (zero-mean/unit-biased-variance) before calculating
autocorr(x) and
crosscorr(x,y). The results are biased estimates with unity at zero
lag for the autocorrelation.

To obtain unbiased estimates divide by N-1 instead of N for the
variance and
divide by N-abs(k)-1 instead of N for the kth lag. I didn't like the
resulting plots,
so I use the biased estimate.

To determine significance levels I averaged over M=100 trials for N =
100 dimensional Normal Gaussian time series. The 95th average absolute
value was 0.21 and the 100th was 3.1. Therefore I consider correlation
values >= 0.21 as significant.

A noise-free nth order polynomial can be determined by n+1 points.
when I imagine a nth order polynomial fit to a smoothed plot of x, or
y vs x, I start thinking about nonzero lags <= n+1.

Hope this helps.