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I have dataset with size 4630 and I used KPSS test to check if it is stationary or not. I get on this output, Is that mean the value of p_value is not correct? or how can test large values with kpss test?

InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

warnings.warn(
KPSS Statistic: 1.500480764853612
p-value: 0.01
Critial Values:
   10% : 0.347
   5% : 0.463
   2.5% : 0.574
   1% : 0.739
Result: The series is not stationary
ayla
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  • The warning seems clear: the p-value of the test is less than 1%. It doesn't know how much less, but since most people don't usually require such low levels anyway, in practice it shouldn't matter: the test is rejected. Do you really need to know the p-value? – Chris Haug Jul 27 '22 at 13:59
  • In this case, is the test results considered correct? Can I use it as a correct result? Is there a way to know the exact value of p-value ? – ayla Jul 27 '22 at 16:00
  • Whether the test results are considered "correct" is completely independent of the results presented here. We can't know whether the results are correct based on what you've shown. There's not anything intrinsically wrong with this result, and in fact this function will never return an "exact" p-value: the critical values shown are based on Monte Carlo experiments and quoted from the original KPSS paper, and when the p-value would fall within the table, it is interpolated from it, so it's always an estimate. – Chris Haug Jul 27 '22 at 16:16
  • Ok, Thanks, As long as the estimated value of the p-value is less than 0,01 and 0.01<0.05, so it is not stationary. Is that correct? – ayla Jul 27 '22 at 16:34
  • If the data is large, for example 5000, are these tests be not accurate? – ayla Jul 27 '22 at 16:55
  • closely related: https://stats.stackexchange.com/questions/581467/testing-by-using-kpss/581577#581577 – Christoph Hanck Jul 28 '22 at 11:54

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