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I have time series data and I want to know whether preserving only a limited portion (say first 300 seconds) and discarding the rest would still leave me with a good estimate of the shape and spread of the data's distribution or do I end up losing too much information.

To do this I am using a 2 sample ks test. I use all the data points for the first 300 seconds as sample 1 and the whole time series (varying lengths from 300 to 6000 seconds) for the second sample. So sample 2 contains sample 1 + additional data. Is this approach correct?

Note that I have millisecond level data, so the sample size is quite large. Also, I understand that the ks test does not account for the inter-dependency of data within the time series, but my data is simulated so I am working under the assumption that if the shape and spread is preserved, it should be enough.

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The problem with your experiment is that your samples come from the same signal and, therefore, cannot be regarded as independent. This will prevent you from using a standard KS test so you must find alternatives for dependent samples. Considering this sorted, your experiment would be correct if we were to assume that identical distributions between samples would imply similar information patters and, by extension, no information loss in your signal. To be on the safe side with that ambitious assumption, you should perhaps set up another hypothesis test to compare the variances of the two dependent samples. If you don't see significant differences in neither distribution nor variance, then you should be alright.

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  • $\begingroup$ I understand why my test might be insufficient. But I don't quite understand, how does comparing the variance add value? Doesn't the KS test already sort of cover the variance from mean in the form of CDF. $\endgroup$ – saby Nov 21 '15 at 21:07
  • $\begingroup$ Similar distribution does not guarantee similar variance. It's a different test, which in my opinion would add a lot of value. $\endgroup$ – Digio Nov 24 '15 at 10:12

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