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Thread Subject:
Significance Levels for Correlation Functions

Subject: Significance Levels for Correlation Functions

From: Greg Heath

Date: 19 Oct, 2012 01:47:05

Message: 1 of 2

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.
Therefore
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.

Greg

Subject: Significance Levels for Correlation Functions

From: Greg Heath

Date: 20 Jan, 2013 14:00:09

Message: 2 of 2

Greg Heath <g.heath@verizon.net> wrote in message <aa1a73b0-e475-4c56-a378-43bd1266ef63@y5g2000pbi.googlegroups.com>...
> 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.
> Therefore
> 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.
>
> Greg

sigthresh95(N) is a function of N.

I repeated the N=100 experiment for M = 100 and M=1000. I now get

sigthresh95(100) ~ 0.15 %(NOT 0.21 !)

Hope this helps as a check for your calculations.

Greg

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