All of my textbooks mention restrictions for AD models but don't explicitly say what they mean by "restrictions" and I'm having a hard time grasping what they mean.
$y_t = \beta_0 +\phi y_{t-1} + x_{t}\beta_1 + x_{t-1}\beta_2 + error$
Would the only restrictions be that:
$\beta_2 = \phi\beta_1$ which means that $\beta_2 - \beta_1 = 0$?
Also, is $\phi < 1$ a restriction? And am I missing anything?
If someone could clarify what texts are assuming when they say "parameter restrictions" it would be very helpful. Thanks!
You generally need $$|\phi| < 1$$ for stability.
Not sure why you need $\beta_2 = \phi \beta_1$ unless you have to meet some dc gain, i.e. if $x_t$ is a constant and no error, you want $y_t$ a constant equal to $x$.
Not sure what $\beta_0$ is except as the bias in the error.