# Inference in cointegated VAR model

I am estimating the following VAR model:

$$\begin{equation*} x_t = k + A_1 x_{t-1} + A_2 x_{t-2} + \dots + A_p x_{t-p} + \epsilon_t, \end{equation*}$$ where $$x_t$$ is a vector of variables and notation is standard. I have three variables in $$x_t$$: Two $$I(1)$$ processes and one $$I(0)$$ process. The Johansen cointegration test yields rank 1, such that there is one cointegrating relationship.

I am aware that if I rewrite the model to a vector error correction model (VECM), then inference is valid on the parameters using t-values and standard normal distributions.

My question, however, is whether (standard) inference is available directly on the parameters of the VAR model, that is $$A_1,A_2,\dots,A_p$$, given cointegration?

Thank you!