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I'm running the augmented Dickey-Fuller-Test for two different Time Series and I have a question about the results in column "Variable". Why is there sometimes Y(-1) and D(Y(-1)) and sometimes only Y(-1)? And can I use the same detrending method for both time series?

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and

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The difference follows the different lag length. In the first case the lag length is 1 and in the second the lag length is 0. The program (Eviews?) calculated the lag length automatically based on AIC. You can also determine it manually.

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  • $\begingroup$ Thank you for your answer and yes it's Eviews. So in the second picture the time series only follows a trend while in the first picture the time series follows and trend and also depends on the value of the last period? $\endgroup$ – PAS Oct 11 '17 at 14:01
  • $\begingroup$ The test-statistic of a adf-test follows y(t)-y(t-1)=D(Y(t))=c+ay(t-1)+bD(Y(t-1))+d*trend. If you have a lag then you input D(Y(t-1)) in your equation. C is the intercept. But you have no trend in your tests. $\endgroup$ – Klaus Oct 11 '17 at 14:14
  • $\begingroup$ What do you mean with "I have no trend"? Do you mean "no trend" regarding D(Y(t-1)) because both time series definitely have a unit root (and therefore a stochastic trend) but only based on Y(-1) (or is this statement totally wrong?) $\endgroup$ – PAS Oct 11 '17 at 14:38
  • $\begingroup$ In your test statistic, you have no deterministic trend. But you a right, you have a unit root (stochatsic trend) in both equations. $\endgroup$ – Klaus Oct 11 '17 at 15:04
  • $\begingroup$ Thank you again. Maybe the last question: Which detrending method is the best for a time series with a stochastic trend? $\endgroup$ – PAS Oct 11 '17 at 15:16

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