secret sauce says for an AR(1) model to be covariance stationary: b1 must be less than one and if b1 is equal to one there’s a unit root. can’t b1 also be greater than 1?
basically them model is not covariance stationary of b0 / 1 - b1 = undefined…if your slope is one then you have non stationarity…and you would do an AR(2)
Also, a nasty trick… not only do you need to make sure that b1 does not equal 1 – but you need to test the statistical signifance of b1 to make sure it is statistically significantly different from 1. Otherwise you cannot reject the null hypothesis. As for having to go to an AR 2 model, is that the correct solution? I thought you go to first differencing.
i know that when b1 = 1 its undefined. i am asking why b1 being greater than 1 is not ok? is it because it would make the mean reveryting level negative?
mcf… my bad…absolutely right… first differencing!! too many red bulls…
“i know that when b1 = 1 its undefined. i am asking why b1 being greater than 1 is not ok? is it because it would make the mean reveryting level negative?” I was wondering the same thing, if someone could answer this specific question I’d appreciate it.
yes if you have a unit root you first difference, correct
when b1>1 the AR(1) model is not mean-reverting and not covariance stationary.
why
I gave a short proof on this thread. Read it and ask a question if you still don’t understand why. http://www.analystforum.com/phorums/read.php?12,972199,972211#msg-972211
it’s something called an exploding root. don’t think we need to know this for the exam.
the show NY Wrote: ------------------------------------------------------- > why how can it be mean-reverting when it just keeps growing? what is the mean? the variance?
what supersharp says is all you need to know to answer what if b>1.
dynamutt Wrote: ------------------------------------------------------- > it’s something called an exploding root. don’t > think we need to know this for the exam. very good dyna …this is correct
“b1 can’t be more than 1” works for me
It can but then you will have a growing trend… think of slope larger than 1. Or here is a not so perfect anaology, but it should do. You have $100. If you multiply it by less than 1.0 every day, guess where it’s gonna go? Try it. If you multiply it by 1.5 every day, then you’ll be very rich very soon. Your series would not be covariance stationary but you would become rich.
holy crap it just clicked, thanks