Let's say I have carried out two experiments where something was changed in one compared to the other. I measure a feature in each experiment and therefore have the two time series for this feature, let's call them x_i and y_i. They are both assumed to be non-stationary (think of some logistic growth with added noise). I would like to show, with a statistics test, in the end that there was a difference observed in the two experiments. I thought to subtract the two series i.e. z_i=x_i-y_i and then perform a KPSS test on z_i and then hopefully be able to reject the null-hypothesis that z_i is trend stationary, whereby I would then conclude that there are different trends in my two time-series. Any comments on this approach? Is it flawed?
Test to show that the underlying process of two non-stationary time-series are different?
$\begingroup$ "Different" is a rather vague notion when it comes to statistical testing. It would be easier to come up with a test if you had a concrete type of difference in mind, e.g. a difference in means, a difference in variances or something like that. $\endgroup$– Richard HardyJun 5, 2022 at 6:04