Testing whether two timeseries samples are from the same population

Question

I would like to test if different timeseries samples (over the same period of time) are plausibly from the same population.

e.g. popularity of movie Avengers over time from different websites. The expectation is that the trend over time would be similar on different websites, and if one website has a trend that's markedly different, it may signal manipulation.

I'm looking for something like a "t-test" but for a timeseries. How would I do this?

Thanks!

Answer 1

Look at the green's function for both the data sets, if they have similar behavior i.e. similar kind of AR and MA roots, then you can say they both come from a similar system, else they come from different systems all together.