I am using cross correlation to demonstrate a potential link between two time series (ext & co). Both series are strongly autocorrelated, so it is difficult to assess the dependence between the two series. For a quick preliminary analysis, the cross correlation shows a clear (somehow delayed) link between the two time series, although it might spurious. 
. Prewhitening seems to be the best option; I will prewhiten my x variable by fitting an ARIMA process and then use the coefficients to filter my variable y. My question is if I should estimate the coefficients of the ARIMA process (for example using auto.arima) using my series x or by using the residuals of the OLS regression of x on y.
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1$\begingroup$ If you are primarily interested in a link between two time series (and not their transformations), will you be answering the right question if you use prewhitened data?.. $\endgroup$– Richard HardyJan 13, 2016 at 20:23
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$\begingroup$ Yes the right question is being answered though a single filter pre-whitening operation (not two filters !) . See onlinecourses.science.psu.edu/stat510/node/75 for a basic ( largely correct) primer on this approach. Note that the single filter does not distort but amplifies any predictive relationship between the two original series. $\endgroup$– IrishStatJan 13, 2016 at 22:45
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$\begingroup$ Not quite. If two series share a common trend (stochastic or deterministic) and this trend is removed by prewhitening, you will entirely miss the obvious connection between the series. $\endgroup$– Richard HardyApr 16, 2016 at 14:11
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Yes Luigi your approach is the preferred one. The right question is being answered though a single filter pre-whitening operation (not two filters !) . See https://onlinecourses.science.psu.edu/stat510/node/75 for a basic ( largely correct) primer on this approach. Note that the single filter does not distort but clarifies any predictive relationship between the two original series.
answered Jan 13, 2016 at 22:47
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$\begingroup$ HI @IrishStat, this link is broken. Could we consider this updated info online.stat.psu.edu/stat510/lesson/9/9.1 ? $\endgroup$ Jul 24 at 12:55