ayodayo

Unfortunately I don't have the books and can't look at page 305, but you are definitely confused about something I can help clear up.

When we are talking about time series, we are not saying the line has to be a certain angle; you are confusing it with regular regression. Look at the equation we are generating:

y_(t) = a_0 + [a_1 * y_(t-1)]

a_1 is not multiplied by some random t value; it is multiplied by a previous y value! So a_0 and a_1 are essentially weights-- how much value do we place in our previous output (a_1) and how much adjusts the next value back to the mean (a_0 which is determined if a_1 is known).

Let's say our equation is y(t) = 2/3 + 1/3*y(t-1). The mean reverting level is a_0/(1-a_1) = 1. This isn't 45 degrees, that would imply y(5) = 5 or y(6) = 6; instead we are saying if a y is different from 1, the next y should be closer to 1.

I'm not sure if the mean reverting level has to be 1, it's been a while since my test.