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I am checking stationarity or non-stationarity of a time series with R and I am using adf.test and kpss.test in tseries package.

What are the assumptions for these tests?
Is following a Gaussian distribution by the data set one of the assumption?
If yes, what can we do for non-Gaussian time series?

Also, is using the default options for lag order in ADF which is $k = \text{trunc}((\text{length}(x)-1)^{1/3})$ a safe assumption?

Thank you

Ferdi
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Fred
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1 Answers1

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ADF is a parametric test and KPSS is a non-parametric test of unit root. That being said, the chosen lag order in the ADF should be such that residuals are white noise.

Metrics
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  • So it means for KPSS normal distribution is not a assumption but for ADF is? – Fred Mar 18 '13 at 00:25
  • you can find more on that here : `http://stats.stackexchange.com/questions/14076/phillipsperron-unit-root-test-instead-of-adf-test` – Metrics Mar 18 '13 at 01:17
  • @ user1493368 your answer was very helpful for me but Still I am not sure if ADF requires a specific distribution for the data. However I accepted the answer and Thanks a lot. – Fred Mar 19 '13 at 15:08
  • @ Fred : ADF assumes the error term of AR(p) process to be white noise which is a less strong assumption than Gaussian noise. I therefore think that normality is not a requirement. KPSS doesn't assumes the error term to be white noise. – Metrics Mar 19 '13 at 17:03
  • Glad that I was able to help you. – Metrics Mar 19 '13 at 23:43