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I have a Time Series of 336 monthly observations, from January 1987 to December 2014. I'd like to test for differences in uneven (of different size) segments of this time series. In effect, it would be a comparison of smaller time series.

The overall time series exhibits a positive trend, and has to be differenced in order to work with it for an ARIMA (1,1,2) forecasting.

What would be the proper procedure in order to test for differences in the segments, taking into consideration the segments are of different lengths?

Should I differentiate the segments as well, since they are not normally distributed (the overall series, when differentiated, does)? Or should I test for differences with the segments as the come, with a T-test or a different test?

Edit: a simple two tailed mean difference would be enough.

There are also reasons to believe there could be time dependency in the observations of any particular segment.

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  • $\begingroup$ What kind of differences are you looking for? Maybe my answer here could be useful? $\endgroup$
    – Richard Hardy
    Commented Feb 16, 2015 at 6:03
  • $\begingroup$ Nothing too fancy: a different mean with 95% confidence (in either direction, a two tailed test) would be enough. $\endgroup$
    – erasmortg
    Commented Feb 16, 2015 at 6:23
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    $\begingroup$ I suggest you include this information in the original post (both title and body) to help other people understand. I also think my answer (link given above) could actually be relevant for your question. $\endgroup$
    – Richard Hardy
    Commented Feb 16, 2015 at 6:38

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Every difficult problem has at least one incorrect but easy solution. Auto-correlation in the observations creates either an over-statement of the equality of the the two means or an understatement as it depends on the form of the auto-correlation ,thus no simple test of means is appropriate (never mind the impact of anomalies). I suggest that you take the model that you are proposing and use the CHOW test and the QLR Statistic (as your are searching ) to identify the major break point and then proceed to analyze each of the two sets separately. Most times simple approaches are too simple.

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  • $\begingroup$ How about a Wilcoxon test or some of its variations? It allows for relaxing of the assumptions of a T-test and allows for samples of different size.As for the breaking point: It's fixed. I am trying to measure the success of an experiment, this is the reason the segments cannot be moved. $\endgroup$
    – erasmortg
    Commented Feb 16, 2015 at 22:24
  • $\begingroup$ The test you are referring to is a non-parametric version of the paired t test and might work you BUT I am not sure as non-parametric methods are not one of my specialties. $\endgroup$
    – IrishStat
    Commented Feb 16, 2015 at 22:50

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