I need to have in-depth understanding of analyzing the causality and long run relationship between several variables. I am a bit confused, but I can brief that as:
1- all variables shall be integrated, we can use the unit root test
2- then we need to check if these variables are co-integrated using the Johanson test, where the criteria for that test are not clear to me. Here I am wondering if it shall be a pre-condition to have all variables integrated? why do we need to know the order of co-integration? and also, what does the order of co-integration mean?
>> what test shall be applied if variables are non-stationary or stationary at level or different differences?
>>when to use VECM OR VAR?
3- Regarding the Granger causality test, what are the criteria? As I understood, if variables are not co-integrated then there is no causality among them? does this mean these variables are not correlated?
>>>IS this test used to define the dependent and independent variables? therefore should be conducted before any regression model designed?
Your inputs are highly appreciated,,,
Dear Samah
1. Unit root test is used for stationary test of time seriries, Johansen test is used for cointegration test
2. You firstly test the stationary of all variables
- If all stationary at level (I(0)) -> use model like VAR, ARIMA, ARCH, GARCH...
- If all stationary at level 1 -> test conintegration -> exist -> use VECM
- IF they stationary at difference levels -> test cointegration -> exist -> use ARDL
- Otherwise, you take the differences of the non stationary variables -> make them stationary => use VAR or ARCH GARCH
3. The Granger causality is used to testing the causality between 2 variables whether x causes y or y causes x => it provides the empirical evidences just for you sample
Best
Canh
I think you need to differentiate between order of integration which can be tested bya unit root test, and cointegration which reflect long term association between set of variables (two and more). If you decide to use Johansen test for cointegration you need to have all variable of the same order of integration, either I(0), or I(1) or even higher order. But if you decide to use the ARDL test for cointegration it is not required to have all variables be of the same order, they can be either I(0), or I(1) but not more than that. If the variables are cointegrated you need to specify your Granger causality model as ECM form, otherwise specify your Granger causality as VAR model specification.
Best luck
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