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I have two time series related to app usage:

Notifications- a time series of notifications sent to the user from the app.
User Activity- time series of the user interaction on the app.

I am trying to estimate the longitudinal effect of notifications on user activity to answer the question:

Does the nudge cause the user opening the app. And how many hours/days does the effect of a nudge last? That is after having sent a nudge to the user, how long would the user still come back to the app?

I used granger causality test to determine the "granger causality".
Would the significance of the max lag variable be of use in making this estimate?
Is there some other more appropriate way of doing this?

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