If have query about my thesis I have applied OLS technique to examine the determinants of FDI in first step. but I would like to know I can apply cointegration and VECM on same sample size (means on same variables which was included in OLS technique), If yes. then my second problem is on seven variables cointegration not applied means not got results. so I would like to know is there any limit of the variables to apply cointegration. Please suggest me.
First of all, the sample size is also important, but there is no strict limit on the number of variables including into the cointegration model. However, all variables must be cointegrated and this is less likely when you have more variables. You can test the cointegration using for example Johannsen test. The number of co-integration vectors according to Trace statistics or Max-Eigen stat. have to be always one less than the number of variables included into the model. Otherwise variables are not integrated to the same order - not cointegrated.
Sufficient framework for cointergration test under multivariate case is Johansen test.
Eviews software is much simple to run cointergration test compared to other statistical Software. Visit YOUTUBE find VIDEO LECTURES BY hassain OR PHD students lectures in LSE. You will find everything there including analysis in EVIEWS /STATA.
1. First check for stationary.
2. If the variables are non-stationary (have unit root), then use Johansen cointegration test.
3. If they are cointegrated, then use VECM otherwise VAR is the model. Use first differenced variables in VAR as they are non-stationary at level.
In the recent years the fractional integration and cointegration techniques are gaining popularity: fractional techniques are applied for variables which are not I(0) but also not I(1) - somewhere in between. Check Johansen & Nielsen (2012) "Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model". There is a great MATLAB package for that: FCVAR. FCVAR is a special case of VECM. In case of fractional cointegration this may be crucial. Moreover, the variables which are not cointegrated according to the standard cointegration test as in Johansen (1995) may still be fractionally cointegrated.
Coming back to your question, 7 variables should not be a problem, providing you idenitfy which of them enter the cointegration vector.
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