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
    Commented Sep 27, 2010 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
    Commented May 31, 2011 at 20:50

2 Answers 2


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).


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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