Suppose I have a time-series in which I know it to be I(1), but I need to model it with fewer observations. And due to the low power of ADF test, fewer observations means testing the series to be I(0). I believe I should treat the series to be I(1) (e.g. first-difference it) anyway, but I would like to know what is the "kosher" thing to do.
closed as unclear what you're asking by Michael Chernick, Christoph Hanck, Frank Harrell, Peter Flom♦ Apr 26 '18 at 12:27
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If you believe that the data generating process stays constant over time, you can use the longer sample results as an argument for choosing to treat the series as I(1). If you cannot disclose the longer sample to prove the result, you can use subject-matter arguments and/or theories suggesting the series should be I(1). Statistical evidence is just one kind of evidence; it does not mean you cannot use other arguments in the analysis.
Also, note that low power would mean a failure to reject the null hypothesis, and the null hypothesis of the ADF test is that the series is I(1), not I(0). Hence, you cannot say the result you are getting is due to low power.