I am currently investigating the impact of certain indicators such as GDP and inflation on the stock market. However some of my variables are non-stationary and some stationary in levels. All variables are stationary in first differences.
Since I have a mix of I(0) and I(1), I need to take the first difference of the I(1) variables and then use VAR. Say that I have a dependent variable $y$ which is I(0) and independent variables $x_1$ which is I(1) and $x_2$ which is I(0). Do I take the first differences of only $x_1$ and then apply the VAR model? Is that correct?
If I take the first differences, then might I lose the long-run relationship between the variables?
Is ARDL the better method in this case?
If you have any references regarding the above I would be grateful.