# Cross-correlation of two autocorrelated signals (removing autocorrelation with ARIMA)

I want to get the cross-correlation of two time series x and y in R.

I have calculated an ARIMA model, and I can get the mod1$residuals from signal x. These residuals almost have no autocorrelation, so that's great. xts <- ts(x,start=1,frequency=12) #convert to a time series library(fpp) #load forecasting package mod1 <- auto.arima(xts)  I now did the same procedure on signal y. My question is: is this correct? Or should I somehow deduct the mod1 (based on x) from y to de-trend it? ccf(mod1$residuals, mod2\$residuals)


Secondly, I am confused about the order of operations. Should I prewhiten the data before calculating the model?

I found this code:

prewhiten(x, y, x.model = ar.res,ylab="CCF", ...)


Should I estimate the mod1 first and then supply it to the function prewhiten? And are x and y the two time series? Many thanks!

• Related to this. – Richard Hardy Feb 5 '16 at 7:39
• I don't fully understand the answer you point to. Do I remove the arima model from both time series? And do I remove the same model or make two models? – dorien Feb 5 '16 at 9:54
• I know I did not manage to provide a clarification there; I posted the link so that other users could see the background of the question. – Richard Hardy Feb 5 '16 at 10:02
• Regarding terminology, you "estimate" rather than "calculate" model mod1 or ARIMA model. It could be nice to have this fixed in both your question and your answer. – Richard Hardy Feb 7 '16 at 20:04

 print(prewhiten(y, model=mod1))