Suppose I have a time series $x_1, x_2, ..., x_{10}$. I apply the augmented Dickey Fuller test to my data an conclude the data are non-stationary with (say) lag = 2.

With lag = 2, the tested data are $x_3, ..., x_{10}$. My question is: Did I conclude that $x_1, ..., x_{10}$ are non-stationary, or did I conclude $x_3, ..., x_{10}$ are non-stationary?

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    $\begingroup$ All ten data points are used, not just $x_3, \dots, x_{10}$. Consult the wikipedia page for the ADF (en.wikipedia.org/wiki/Augmented_Dickey–Fuller_test) and you can see that for a lag 2 test, $x_1$ and $x_2$ are included in the model formulation when $t=3$. $\endgroup$ – jbowman Jan 4 at 4:13
  • $\begingroup$ Also, like in other inferential tasks, you use the sample to draw conclusions regarding the underlying population/process, so it is really not the sample that is nonstationary (or not), but the underlying process is. Hence, there is no point to make the distinction in your post. $\endgroup$ – Christoph Hanck Jan 4 at 8:34

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