0
$\begingroup$

Consider the AR(1) model y_t=α+βy_(t-1)+e_t Where the errors are white noise N(0, 1). What is the expected value of y_t.

$\endgroup$
0
$\begingroup$

That depends on what you know, i.e.

$E[y_t] = E[\alpha+\beta y_{t-1}+e_t]$

$E[e_t]$ is zero, so

$E[y_t] = \alpha+\beta E[y_{t-1}]$

If you know $y_{t-1}$ then $E[y_t] = \alpha+\beta y_{t-1}$

$\endgroup$
  • $\begingroup$ If it is the unconditional expectation which it seems to be, stationarity is standardly assumed under which Ey_t = Ey_t-1. Using this identity the equation is easy to solve for Ey_t $\endgroup$ – Jesper Hybel Oct 17 at 5:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.