# Nonparametric test for comparing trends in two time series

I am interested in doing a nonparametric hypothesis test in Stata. I have 2 series of data, each time series and that overlap in time period. 10 time periods each.

I am interested in a test that checks whether the series are trending similarly. I am not interested in the levels.

For example, suppose I have a series that happened to obey the equation: y = 2x + 100 and one that obeyed y = 2x + 1. They are clearly very different in level but identical in how they trend. I would want the test to fail to reject any difference in how they are trending in that case. If, however, the series obeyed y = 100, that is trending very differently from y = 2x + 100 despite the common point. Even if it is y = 150 intersects it. I would want the test to tell me that these two series are clearly trending differently.

Is there a nonparametric test for this? I was thinking of something like K-Smirnov, but I cannot seem to figure out how to apply it in Stata to the case at hand.

The alternative I've been doing is a linear regression of y on x for each series and then testing whether the coefficients are statistically different from one another just with the test command (storing the coefficients and then testing).