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Obsidian | Level 7

It was suggested that I also post my question in this subforum.. so:


I want to compare two paired short time series (say of length 10) by comparing their means.


However, two significant issues currently prevent me from doing it:

(1) The data is not normally distributed and the sample sizes are really small, hence relying on the CLT appears to be quite a strong assumption.


(2) The data is autocorrelated.


Both prevent me from doing, e.g. a paired-t test, since the assumptions of normality and i.i.d. observations are violated. I know that I can, for example, perform a non-parametric test such as the Wilcoxon-Rank-Sum test to deal with the first issue. I also know that I can deal with the second issue by, for example, calculating the paired t-test with robust standard erros. However, the Wilcoxon-Rank-Sum test still requires independence, and calculating robust standard errors still requires normality.


Put differently, I do not know how to deal with both issues at once. I would be grateful if anyone could point me towards a procedure that deals with both issues.

Opal | Level 21

Note that if you are contemplating a paired test, you only need the paired differences to be normally distributed.


To account for autocorrelation, you could specify a model such as


MODEL myPairedDiff = / nlag=1;


i.e. fit an intercept only model to the paired differences, in proc autoreg (part of SAS/ETS).



Obsidian | Level 7

Thanks for your reply. I am aware of the statement regarding the normality.


What exactly does the model you suggested lead to?


I was thinking to estimate an intercept only model of the differences, and then computing a t-test with robust standard errors of the estimated coefficient. Since it is an intercept only model, this is basically just a paired t-test with robust standard errors. Is that what you are suggesting?


However, the differences are NOT normally distributed and I am unsure of how to account for that.

Opal | Level 21

I am sure you already considered transforming your data. Beyond that, I just don't know what else to try, sorry. 

Obsidian | Level 7

I would really appreciate a reply. Thank you.



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