Hi! According to Sjö (2011), https://www.iei.liu.se/nek/730A16/filarkiv/1.307105/Dfdistab8.pdf, the Pantula principle should first start with a constant and a trend, and then work its way towards no constant or trend. This is counter to what I have learnt. In my econometrics course, it says the Pantula principle should start with no constant or trend, and end with constant and trend. What is correct?
You should try all the cases: none, intercept, intercept and trend. A variable is stationary even if one of the cases shows that.
It is a good strategy to start with the model containing both a constant and
a trend, because this model is the least restricted. If a unit root is rejected here,
due to a significant p, there is no need to continue testing.
Also. Dolado procedures tells that you should start from ''with trend and intercept'' then 'with intercept but no trend'' then 'no interecpt and no trend'' and stop where you find the series is stationary. you can learn more details in ENDERS APPLIED TIME SERIES.
See Cointegration Analysis in Econometric Modelling by RICHARD HARRIS ( see 96 through 97) 1995 for an example and step-by- step illustration of Pantula Principle. in a nutshell, it is to start with the most restrictive model (no linear trend in data (Table in Osterward ending in 9.24. OR 28.14, 22.00, 15.67 and 9.24. That is, the restricted intercept in CE; and none in VAR and CE
then, to Linear trends in the levels of the data (Osterwald Table ending in 3.76 or the the one that ends in 8.18 (the assumption is no intercept in CE and test VAR but there is trend in CE. It often referred to as an unrestricted constant model.
Here, one may introduce a model under the assumption of no intercept in CE and test VAR, but there is a trend in CE and use a Table in Osterwald ending in 8.18.
Last, is the no quadratic trends in the levels of the data (Osterwald ending in 12.15. The critical values are reported as follows 31.46, 25. 54, 18. 96 and 12.25 for the 5%.
In these models, you stop the first time the null hypothesis is not rejected. That is, starting from the first model you move through the maximal eigenvalue row by row. I do not consider the two other extremes because they are rare in applications.
https://knowledge4policy.ec.europa.eu/publication/variable-selection-regression-models-using-global-sensitivity-analysis_en