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Significance Levels for Correlation Functions
Posted:
Oct 18, 2012 9:47 PM


I standardize (zeromean/unitbiasedvariance) 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 N1 instead of N for the variance and divide by Nabs(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 noisefree 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



