# Vector autoregression for mix of stationary and nonstationary variables

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.

My question:

1. 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?

2. If I take the first differences, then might I lose the long-run relationship between the variables?

3. Is ARDL the better method in this case?

If you have any references regarding the above I would be grateful.

• I have answered a related question here. – Richard Hardy Jan 31 '16 at 13:28

1. In your example there is only one integrated variable, $x_1$; hence, taking the first differences of $x_1$ and leaving the other variables $y$ and $x_2$ in levels before estimating a VAR model is fine. But if you had more than one integrated variable, you should consider cointegration.