Here are some potential ways to think about this:
A quick and dirty way to deal with autocorrelation is apply a difference operator to each series in the hope of inducing stationarity. You could then look at differences in differences (DiD) to compare the two series, and waving your hands to imply that these are iid variables now. Then a straight t test or a Wilcoxon test might have some validity. You would not be able to say that the two series were different (as they may have level differences), but you could make inferences regarding the shape of the series relative to one another. However, if the differences between series is multiplicative, this may lead to an incorrect inference (i.e. the means of the differences do not differ. but the variances are not equal). As an example, consider that series 2 is simply 2*series 1 at each point. A DiD analysis will tell you that the means are not different. If the series are now stationary, both series of differences should have mean=0.
If you had more than 2 series, you might look at PROC COPULA, but once again there is an assumption regarding normality (or in this case multivariate normality).
If you had multiple measures at each time point in the series, you could fit a generalized mixed model or GEE model with correlated errors and an appropriate distribution.With only a single measure at each time point, you could only fit a main effects model using these tools, and would have to assume that the time component was identical for the two series (no interaction).
My last suggestion would be to try to bootstrap this, but with only 2 measures at each point, you can't really generate a lot of samples. You probably could bootstrap the differences between the series to get an approximation to the distribution of differences, and see where your sample falls in that distribution.
If none of these seem to fit, then you should follow @Ksharp's suggestion and post this in the Forecasting community, and see what those guys suggest.
SteveDenham
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