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How do you tell if the correlations at different lags obtained from the cross-correlation (ccf function) of two time series are significant.

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    $\begingroup$ Have a look at my question here: stats.stackexchange.com/questions/1881/… $\endgroup$ – nico Sep 27 '10 at 16:35
  • $\begingroup$ hi. I have one question. How can I test the significance of the correlation coefficient? I have two time series and I want to test if they are cross correlation . should I do prewhitening the two series before comuputing the ccf or there are an easy way? $\endgroup$ – user4823 May 31 '11 at 20:50
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The variance of the cross-correlation coefficient under the null hypothesis of zero correlation is approx $1/n$ where $n$ is the length of the series. The coefficients are also asymptotically normal. So approximate critical values (at the 5% level) are $\pm 2/\sqrt{n}$.

These critical values are plotted automatically in R using ccf(x,y).

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The cross-correlation coefficient does not measure dependence between time series. The proper tool for it is the coherence function. For example, see Bendat and Piersol, 2010.

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  • $\begingroup$ Do you mean Bendat and Piersol, 2000. Single-Input/Output Relationships. I could not find any article from those authors in 2010. $\endgroup$ – have fun Mar 2 '18 at 10:28

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