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I am trying to find the correlation between two time series, call them A and B. Let's pretend A has the number of successful advertising campaigns for each month for a company, and B has the company's revenue growth rates (year over year) each quarter. My hypothesis is that the effects of a successful advertising campaign would show up next quarter, and that there would be a lingering effect for about a year.

Based on my assumptions, would it be legitimate for me to try to cross-correlate the values in B and a moving average over a year shifted forward one quarter for the values in A? If not, why not, and what would be a legitimate way for me to test my hypothesis? I am using R, but am looking to make sure I am thinking about this correctly statistically.

Thanks so much for your help.

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Yes, doing a cross-correlation is probably what you want to do. If your hypothesis is correct, the cross-correlation function will peak at a lag of 1Q and slowly die away over the next few quarters.

However, interpreting correlation functions can be tricky, especially when you want to consider the uncertainties and significance. The points in the correlation function are NOT independent. There are a lot of things affecting quarterly sales besides advertising so you may need many-many years to see a significant effect. This would work much better if you had hundreds of companies to work with. I doubt that you will see any significant effect from one company over a handful of years especially the last few years which had so much volatility.

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  • $\begingroup$ Yes! I agree with you about the example - this one is purely hypothetical. I am wondering, however, would it be legitimate to take a cross-correlation between a moving average and a regular time series? Also, does it mess anything up if my predicted variable is a growth rate? I am assuming this just changes the interpretation, but wanted to make sure there wasn't something I was overlooking that might screw up the validity. $\endgroup$
    – overflowname
    Mar 19, 2014 at 1:35
  • $\begingroup$ I would not take a moving average. You don't really need to. Just calculate the cross-correlation function on a quarterly basis. If you signal is large enough (I have doubts) the function will peak at 1Q and drop off from there. If you really want to you could rebin the correlation function over 4 bins but I don't think that will buy you much in terms of statistics. If there were no correlation between the points, it buys you only a factor of sqrt(4)=2 in error. $\endgroup$
    – Dave31415
    Mar 19, 2014 at 1:42
  • $\begingroup$ But they are very correlated and so it will be much less. $\endgroup$
    – Dave31415
    Mar 19, 2014 at 1:43
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    $\begingroup$ The lingering effect is a hypothesis. If you just keep everything on a quarter basis, you will test whether it does drop off each quarter by looking at the profile. The measurements of the cross-correlation function at different lags already accounts for this effect. $\endgroup$
    – Dave31415
    Mar 19, 2014 at 3:08
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    $\begingroup$ Well you asked about whether it made sense to do explicit regression instead of a correlation function. I said that they are very similar but not exactly the same. They can be made to be the same if you subtract off the mean first. That is all. $\endgroup$
    – Dave31415
    Mar 22, 2014 at 0:35

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