I perform some time series fitting with the help of the forecast and urca packages. I have a question regarding the corespondance between results coming from statistical test such as KPSS, ADF or ERS, and the results arising from automatical selection procedures such as auto.arima from the forecast package.
Suppose we are in a situation where the outcome of the KPSS test is that the series does not need to be differentiated. I then apply the ADF test, which shows that the series is stationnary up to a trend (at+b).
In that situation, I could force the auto.arima function to consider only ARIMA models that include a linear trend, but I can also explore all the models (including or not the trend) and let auto.arima choose the best one. And there are cases where the outcome is in contradiction with the test result, e.g. the chosen model does not include a trend while the test advises to include one.
What is the best practice in such a case ? Should the test result be prevalent to the selection of the ARIMA model, or is it best to consider all possible models and choose the best one ?
