Hi, Salam Munirah Mamdouh

The application of a VAR model with time series of integration orders I(1) and I(2) can lead to the violation of several fundamental assumptions. These include homoscedasticity, non-collinearity, normality of residuals, and absence of autocorrelation, not to mention stationarity. Such violations can result in biased outcomes and misleading interpretations of the estimated coefficients. Therefore, it is advisable to consider alternative models, such as VECM models, contingent upon confirming cointegration, or ARDL models, which offer greater flexibility in handling time series data.

For a detailed explanation of integration and cointegration of variables, please refer to my document titled "Integration and Cointegration of Variables" available at : Article Integration and Cointegration of Variables (ICV)

Warm regards,

Before you do any econometrics you must have some theoretical model that you wish to estimate or have some other question or procedure (for example forecasting) that you wish to examine. This must make economic sense.

There is no way that a single I(2) variable can be used to explain and I(1) variable.

There is no way that a single I(2) variable can be explained by a group of I(1) variables.

Now consider that the first difference of an I(2) variable is I(1). thus if you take your I(1) variables and the first difference of your I(2) variable all your variables here are I(1) and you may do cointegration analysis. If there is cointegration you can use a VECM or similar. If there is no cointegration reduce all variables to I(0) by taking first differences and use a VAR.

All of this is contingent on it making economic sense. It may be the case that if you integrate one (or more) of your I(1) variables you may get a cointegration relationship that a combination of I(2) variables to I(1). This gets complicated and you may need to get some detailed knowledge of what to do then. It all depends on what you are trying to achieve. No one can give you an answer unless you explain. Suggestions such as the above may be misleading.