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.
Solved – Cross Correlation and Prewhitening
arimacross correlationrregressiontime series
Related Solutions
Pre-whitening is definitely the way to go. It does not change the relationship but enables identification of the relationship between the original series.. Care should be taken to identify any deterministic structure in the original series and develop the pre-whitening filters in conjunction with them . See http://viewer.zmags.com/publication/9d4dc62a#/9d4dc62a/66 for a review which highlights Transfer Function identification. If you wish you can post your data in an excel format and I will try and explain each step.
EDITED AFTER RECEIPT OF DATA:
120 values for Y (STOCK1) and X (STOCK2) were analyzed utilizing https://onlinecourses.science.psu.edu/stat510/node/75 guidelines using an automatic option available in AUTOBOX http://www.autobox.com/cms/ a commercially available system which I have helped develop. Modelling is an iterative,self-checking process, which extracts structure from the data (with possible model pre-specification) and culminates in a parsimonious equation. I will try and walk through the steps showing details from the automatic process which is faithful to the PSU reference.
The intial pre-whitening filters for X and Y are shown here 
.
Each of the two series is non-stationary and each one required one order of differencing to obtain stationarity.
The pre-whitened cross-correlations and proportional Impulse Response Weights are 
. AUTOBOX in a conservative mode INITALLY suggests 1 lag in the differnce of X 
. estimation and diagnostic checking 
suggests the need to add a second lag to the model .
. Intervention detection examines the need to accomodate unspecified deterministic structure and suggests a pulse at period 8 
which is not significant. Step-down leads to the fina
l model and here 
. The model's residuals are plotted here 
. The Actual/Fit and For
ecast (based upon future expectations of X and the model) are here .
All Transfer Functons can be expressed as Regression-type equations aiding interpretation by humans. The model in this form is 
Prewhitening seems like a good way to help interpret ccf. (see here)
Prewhitening basically estimates a model (such as ARIMA) on data1, then the residuals data2 and this model are used in a ccf function with data1 residuals. In the case of this question:
print(prewhiten(y, model=mod1))
will display the ccf graph
Best Answer
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.