here is something i never quite understand
say we want our AR model to have stationary covariance, which is constant expected value, variance , and variance with lagged and leading values
How is that the test of this comes down to unit root test by Dickey Fuller, which is just if b0=1, is that because constance covariance is definied by mean reversion so if b1 not equal to 1 is then enough??
Mean reversion level is known as
b0 / ( 1 - b1)
If b1 = 1, then there is no mean reversion (unit root), the time series is not covariance stationary
Not having a unit root is a necessary but not sufficient condition for covariance stationary. To wit, if unit root is not present, then the time series has constant mean. However, the covariance and variance may not be constant.
_ How is that the test of this comes down to unit root test by Dickey Fuller, which is just if b0=1, is that because constance covariance is definied by mean reversion so if b1 not equal to 1 is then enough?? _
This is not the case. Dickey Fuller is testing if g=0 where g is defined by (b1-1). Remember a time series is covariance stationary if is has a finite mean reverting level defined by b0/(1-b1). Since you cannot divide by 0, you must test if b1 is significanly different than 1 which is what Dickey Fuller does. If we test it and Dickey Fuller says that B1 is statistically different than 1 - then now we know that we are not dividing by 0 and thus we have a finite mean reverting level.
You will love the Quote function… 
You will love the Quote function…
Bah, it’s overrated.
