Consider that I have a weakly stationary series for the period 2003M1-2014M12. I want to make a VAR model for the subsample 2007M1-2014M12.
Should I reconsider the weak stationarity of my series, so test for unit roots and if necessary, take first differences? Or should I assume that my series is still stationary?
If you assume that the data generating process (DGP) was the same throughout the whole sample, then using the full sample gives more power to tests of stationarity of nonstationarity. Therefore, you should rely on the test results from the full sample.
If you assume that the DGP might have been changing over time within the sample, you may want to conduct stationarity or nonstationarity tests on the subsample you will actually be dealing with. However, note that if you cannot reject stationarity for the whole sample, then a subsample is also likely to be stationary. This is in contrast to finding stationary subsamples, which does not imply the whole sample is stationary; e.g., there could still be level shifts between mutually exclusive subsamples.
