Let me know if this is a duplicate.

This seems to differ from other time series questions I've seen in that I'm not trying to forecast the future. Maybe that will mean only a difference in the application but not the math itself -- not sure. I'm new to time series analysis in general (besides basics like moving averages, etc.), though I'm familiar with basic frequentism.

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The scenario is that I have two time series variables. One variable could be number of google searches per day in the US for "Game of Thrones". The other could be the same thing, but in Europe.

One is strongly predictive of the other . They both fluctuate significantly, but do so together -- at a glance, it's rare that Europe is less than 25% or more than 30% the number of google searches in a day than the US on that same day.

I have lots of data from both countries on the same days. But say next week I want to use the US search numbers to predict Europe's numbers for that same week without looking. How could I produce interval bands of some sort such that Europe that week should lie within those bands with some guarantee, perhaps due to some (credible) parametric assumptions?

One case where this might be interesting is in a quasi-experimental setting. There's some intervention -- maybe Game of Thrones becomes rated R in Europe and I want to see if this caused Europe's time series to go outside of these bands. I want to "see" if Europe ceases to behave how we would expect based on what we're seeing in the US.

Looking for simpler, tried and true approaches (maybe Bayesian if that helps), rather than cutting edge. Hopefully something that's easy for me to briefly justify to non-math people.


  • $\begingroup$ why don't you actually post the two time series and specifically detail a question. $\endgroup$
    – IrishStat
    Jul 10, 2019 at 10:14
  • $\begingroup$ graphs are good ...data is better and mandatory to fully inform you ! $\endgroup$
    – IrishStat
    Jul 10, 2019 at 18:50

1 Answer 1


You seem to be looking for a , not a . There is a difference.

The simplest approach would be to regress the European numbers on the US numbers and use established formulas for regression PIs. Maybe work on a log scale, since you anticipate a multiplicative relationship. (Note that you need a bias correction in back-transforming an expectation prediction from the log scale, but you don't need it in back-transforming a PI.)

Alternatively, try a regression as above, but model residuals using ARIMA to capture any remaining time series dynamics. The forecast package for R will do this for you and give you PIs.


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