 # Covariance Stationary

mwvt9 Wrote: ------------------------------------------------------- > #4 is not a typo. > > In order to test if b1=1 you have to perform a > dickey-Fuller test (exactly why is beyond our > scope). This says that you have to take b1-1 and > figure out if it is equal to 0 or not. > > If b1 is less than zero than not a unit root. If > b1 is equal to zero than you have a unit root. Schweser SS says it wrong…it should read that b1 must be less than ONE (not Zero)!! and thats what he was asking?? 4) The Secrect Sauce says for an AR1 model to be covariance stationary, b1 must be less than zero. Is this right? - I thought it just needed to be less than 1. Anish

I think B1 can be less than 0 because your mean reverting level would be: Bo / (1 - B1) As long as B1 is not 1, you don’t have a unit root problem. If B1 is greater than 1 then you have an explosive root. If B1 = 0 then mean reverting level will be: Bo/1 ----> I don’t see what the issue with that would be.

^^ If b1=0 then you won’t have any independent variable bro… Anish

oops, haha yea your right. so basically, B1 can’t be 1 or 0

True =)

One possible exception, I thought b1 could be 0 after first-differencing corrected to make it stationary. Thoughts? (Looking at top of pg 26 in the Secret Sauce)

JoeyDVivre Wrote: ------------------------------------------------------- > > This might be - I would say testing whther b1=1 or > b1 - 1 = 0 is about the same. True, but in order to test whether b1 is equal to 1 you would have to run a t-test on the coefficient. Schweser says this can’t be done for statistical reasons. Maybe you know what that means, but I don’t. So they say Dickey and full got around this with the test they devised, which is basically subtracting one from the coeff. So instead of a t-test of 1-0/se Ho=1 Dickey fuller says 1-1/se Ho=0

anishcandy Wrote: ------------------------------------------------------- > mwvt9 Wrote: > -------------------------------------------------- > ----- > > #4 is not a typo. > > > > In order to test if b1=1 you have to perform a > > dickey-Fuller test (exactly why is beyond our > > scope). This says that you have to take b1-1 > and > > figure out if it is equal to 0 or not. > > > > If b1 is less than zero than not a unit root. > If > > b1 is equal to zero than you have a unit root. > > > Schweser SS says it wrong…it should read that b1 > must be less than ONE (not Zero)!! and thats what > he was asking?? > > 4) The Secrect Sauce says for an AR1 model to be > covariance stationary, b1 must be less than zero. > Is this right? - I thought it just needed to be > less than 1. > They are basically equivalent. Look up the Dickey Fuller test for confirmation. > > Anish

mwvt9- From what i remember from the CFAI text, I think the Dickey Fuller Test calculates the statistic similar to the conventional t-statistic. It is only the t values that have been modified for this test by D-F. So the interpretation of the hypothesis is no way different from that of the usual t-test. So the null hypotesis i.e b1 = 1 is calculated in the usual way (i.e b1 -1 / Std Error) and this t-statistic is calulated against the modified t-values calculated by D-F.