Basically, I have five time series. All are stationary. Now, let's call them $Y$, and $X_1$ to $X_4$.
Normally you'd do $$ Y_{t} = \alpha + \beta_1 Y_{t-1} + \beta_2 X_{1,t-1} + \epsilon $$ and this could be redone for $X_2$ to $X_4$. But is it possible to just do $$ Y_{t} = \alpha + \beta_0 Y_{t-1} + \beta_1 X_{1,t-1} + \beta_2 X_{2,t-1} + \beta_3 X_{3,t-1} + \beta_4 X_{4,t-1} + \epsilon \ ? $$ Will the $F$-test still be valid?