st: Nonparametric testing between two series

[Jessie C <jessiecoh@gmail.com>]

I have 2 series of data that are time series.  I want to test whether
the 2 series trend in a similar direction or not statistically.  I'm
not interested in the differences in the levels between the two series
but only the difference in how the series is trending.

For example, if one series is trending upwards and the other is
trending flat, then I'd clearly like the test to reject that the two
series trend similarly.  If, however, the two series are both fairly
flat, then potentially the test would fail to reject that the two
series trend similarly (or maybe it would reject depending on how
similar the flatness between the two is).  And, moreover, if the one
flat series is pretty much 200 for every data point and the other
series is pretty much 20 for every day point, I wouldn't want the big
difference in their levels to affect the test.

I am blank on ideas.  I'd imagine something like the
Kolmogorov-Smirnov test is what I'm looking to do.  Does that account
for the levels of the series?

I would appreciate any suggestions!  Thank you for your time and help.
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