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I have to compare two time series. Lets say, that I have measurements of temperature from two towns. Now I have to find out if there is a difference in temperatures between this two towns. In another words, I just need something like t-studen test, but for time series. Could you recommend me something?

Thanks, anba

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I would suggest to try to model both time series (ARIMA, seasonal ARIMA) and assess their differences/similarities.

In a sense, you can try to break down all their components; have a look at their ACF, pACF graphs, try to make them stationary, identify the seasonality and so on and all the steps that we usually do when we model time series.

Then if you have evidence that for example an AR(2) model would fit the first time series adequately whereas for the second one you would opt in for an MA(3) then you could say that you have evidence that these 2 time series are different.

The tricky bits would come if you can model both with "similar" models. For instance, if you can use AR(2) for the first and AR(3) for the second. In that case things would be a bit more unclear. If that's the case then the larger the sample the more evidence that they are different. If you don't have "that many" observations then you could say that the hypothesis that these 2 time series are the same cannot be rejected.

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