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I have two time series of daily data. One is sign-ups and the other terminations of subscriptions. I'd like to predict the latter using the information contained in both variables.

Looking at the graph of these series it's obvious that terminations are correlated with multiples of the sign-ups the months before. That is, a spike in sign-ups on May 10th, will lead to an increase in terminations in June 10th, July 10th and August 10th and so on, although the effect wears off.

I'm hoping to get a hint as to which models I might employ to model this specific problem. Any advice would be much appreciated..

So far, I've been thinking a VAR model, but I'm not sure how to include the monthly effect - use a really high order of lags or add a seasonal component somehow?

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What does the CCF plot look like for lags 29 to 31? Are the spikes frequent enough that it shows up? You can use a Granger test to check which lagged values are statistically significant.

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  • $\begingroup$ Yes, there are clear spikes in the CCF plot at lags 28-31, particularly the 30th. $\endgroup$ – wije May 30 '13 at 9:25
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Month level models

You should capture the month level variations in the propensity to terminate (say signups during Christmas holidays are more likely to terminate than signups during April). Let's say your usual time series model is: $$terminations_{t}=\beta_{1} signups_{t-1}+ \beta_{2} signups_{t-2} +..$$ . Now if you believe that the parameters $\beta_{1}$ etc. are month specific you can interact the month indicator flag with the remaining predictors.

Thus your new functional form will be $$terminations_{t}=\beta'_{1} signups_{t-1} MonthFlag_{t-1}+ \beta'_{2} signups_{t-2} MonthFlag_{t-1}+..$$ This is akin to building month-level models allowing greater flexibility in capturing month specific variations in tendency to terminate

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