# Expected value of an AR(1)

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.

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