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I've two groups of data, each containing an equal number of tuples. Each tuple is filled from observations of a phenomenon at regular intervals and are drawn from a discrete set. For each group we are observing independent phenomena, even though in each group they have the same characteristics.

I want to test whether these two groups are created from "different" categories of phenomena.

To make it clearer, let say that group A and group B contains temperature observations over a specified period of time and coming from different places of a country, with locations from group A coming from the north, while those in group B coming from the south.

I want to test whether group A and group B shows a different "behaviour".

Is that possible? I tried to search the Internet and tried to figure out the correct set of terms to search for in order to get some hints, but to no avail.

Thank you for any help.

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I am not quite sure what you mean by showing different behavior. If you mean that they look like different time series then why not fit something like an ARIMA model to each and if the form of the two models are very different you can say that the behavior is different? –  Michael Chernick May 3 '12 at 20:39
    
How would you state the sentence "if the form of the two models are very different you can say that the behavior is different" formally? –  Cristiano Paris May 3 '12 at 20:59
    
@MichaelChernick See my comment here to understand why I converted your reply as a comment. –  chl May 3 '12 at 21:09
    
So you want to know if they might both be realizations of the same generating stochastic process? –  JohnRos May 6 '12 at 23:20

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