I am having a distribution of time delta between temporally successive events.

I found that these observations are dependent on neighbours with small lag (ACF and PACF show high significance), hence I can not assume independence in my data.

I further wish to test for the difference between two such distributions, which are drawn from temporally distanced samples.

I consider using Kolmogorov-Smirnov criterion.

Question: is the KS-test free of the independence assumption (not between samples, but rather between observations is a sample)? What approach could do well in my situation?



1 Answer 1


No, it is not. The derivation of the null distribution for the KS statistic relies on IID. (It may be robust against some violations of this assumption, but I don't know of any studies of that.)

If you don't care about whether the distributions are different in the small-time-lag region for which you observe correlations, you could KS test the truncated distributions.

  • $\begingroup$ Hi David,Thank you for this hint. So, I do violate assumptions if go straight ahead. By truncating my sample, do you think taking a sparse sub-sample (thus destructing the temporal neighbour-sequence) is a workaround? I think I try that and check the PACF. Alexey $\endgroup$ Jun 20, 2017 at 8:56

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