Most of the text I have read on stationarity and co-integration will say that if the variables in a model are not co-integrated, the model will be spurious. But I need to know what I should do if one of the core variables in my time series model that intends to find how the variables are related is integrated of different order with the rest of the variables (including the dependent variable).?
The question is not really clear. But if you are studying the causal relationships between various variables and if you have some variables I(0) and others I(1), you should use the ARDL cointegration bounds testing approach.
With the time series data, the first approach is to check the order of integration. Order of integration of different variables should be checked after taking log. If the variables come out to be integrated of different order, then ARDL is the right approach as suggested by Mounir Belloumi.
what do you want to do?
the question is not yet clear, please help me to answer the question
If the order of integration is not the same (some variables are I (1) and others are I (0)), different solutions are possible :
- Introduce variables I (1) in first differences in the model
- Using a model that incorporates delays non-stationary variables
Thank you all for the interesting answers especially that of Mounir Belloumi. However, I still need a little more clarification.
The standard ARDL bounds test is used only when the series are I(0) and I(1). What happens of if one of the series is I(2)? For instance, if I have Y= I(1), x1=I(0), and x2=I(2) and I want to see the impact of changes in X1 and X2 on Y. What should I do if:
1. I am not interested in the long-run relationship but only the short-run?
2. If I am interested in both the long and the short-run relationship?
3. Also what should I do if the ARDL bounds test show no co-integration (The Ho was not rejected)?
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