Hi all, Can anybody explain how to do this using AR model, what is the test and what is the null etc. Thanks
Dickey Fuller Signficance means not covariance stationary (has a unity root) Null = no unit root.
The Dickey Fuller test is used to test for presence of a unit root. The model is of the form y{t} - y{t-1} = b0 + g1*y{t-1} + et H0: g1 = 0 means it has a unit root and is not stationary. H1: g1 != 0 means it does not have a unit root and is stationary. If you find it does have a unit root, then re-estimate the regression using the form: y{t} - y{t-1} = b0 + b1*(y{t-1}-y{t-2}) + et
futhermore the DF test for unit root by testing this let y(t)=a+bhat* y(t-1) then DF test y(t)- y(t-1) = a+bmod hat * y(t-1) and testing the for the sig of the coefficitent …hope this helps
bobsters Wrote: ------------------------------------------------------- > The Dickey Fuller test is used to test for > presence of a unit root. The model is of the form > > > y{t} - y{t-1} = b0 + g1*y{t-1} + et > > H0: g1 = 0 means it has a unit root and is not > stationary. > H1: g1 != 0 means it does not have a unit root and > is stationary. > > If you find it does have a unit root, then > re-estimate the regression using the form: > > y{t} - y{t-1} = b0 + b1*(y{t-1}-y{t-2}) + et nice one!!!
does unit root = not covariance stationary or can it be one without the other unit root means that b1 = 1 covariance stationary means that mean, covariance, and variance are not constant but i feel like they go hand in hand
unit root = not covariance stationary LOCK (keep the why’s, when’s and why so’s for after the exam)
> covariance stationary means that mean, covariance, and variance are not constant They have to be constant.
thats what i meant, thx
Dickey Fuller Signficance means not covariance stationary (has a unity root) Null = no unit root. So just to comment if it’s significant you are accepting the null hyp and it has a unit root, correct? That means the t calc falls within the acceptance range?
I hate how Schweser has a different dickey-fuller test. They say that you transform the unit root equation x(t)=b0 + b1x(t-1)+epsilon into: y(t)=b0 + (b1-1)x(t-1) + epsilon where b0+(b1-1)x(t-1)=0 and y(t)=x(t)-x(t-1). Then the Ho hypothesis for significance is Ho: b1=1. But on the test, they may ask what their formula is and I have to memorize that in their formula, Ho:b1=0. Now I have to memorize two separate formulas.
Hi all, I read three ways to do this: 1. Plot data and see visually. 2. Use AR model 3. DF test I am Ok with all except #2. I want to know how number 2 test covariance stationarity/unit root? Thanks
I think you just check the printout and see if the regression parameters and the autocorrelations are all insignificant, then it’s unit root. Someone confirm.
rellison Wrote: ------------------------------------------------------- > I hate how Schweser has a different dickey-fuller > test. They say that you transform the unit root > equation > x(t)=b0 + b1x(t-1)+epsilon > into: > y(t)=b0 + (b1-1)x(t-1) + epsilon where > b0+(b1-1)x(t-1)=0 and y(t)=x(t)-x(t-1). > Then the Ho hypothesis for significance is Ho: > b1=1. But on the test, they may ask what their > formula is and I have to memorize that in their > formula, Ho:b1=0. > Now I have to memorize two separate formulas. Its the same concept pretty much. If you accept schweser’s H0: b1-1 = 0, you’re saying b1 = 1, i.e. unit root. If you accept CFAI’s H0: g1 = 0 then think about it: y{t} - y{t-1} = b0 + g1*y{t-1} + et rearrange that to y{t} = b0 + (1 + g1) * y{t-1} + et so if the H0 is that g1 = 0, and you accept it, then the coefficient of y{t-1} = 1, i.e. unit root.
Dreary Wrote: ------------------------------------------------------- > I think you just check the printout and see if the > regression parameters and the autocorrelations are > all insignificant, then it’s unit root. Someone > confirm. unit root means the coefficient of b1 = 1.
Dreary Wrote: ------------------------------------------------------- > I think you just check the printout and see if the > regression parameters and the autocorrelations are > all insignificant, then it’s unit root. Someone > confirm. ‘autocorrelations are all insignificant’, how does this translate into the fact that covariance stationrity exists or unit root doesn’t exists?
autocorrelation of residuals not significant == model correctly specified. Does model correctly specified mean there’s no unit root ?
bobsters Wrote: ------------------------------------------------------- > autocorrelation of residuals not significant == > model correctly specified. > > Does model correctly specified mean there’s no > unit root ? That is what I am looking to be answered. Schweser says three tests for stationarity: 1. Plot data and see visually. 2. Use AR model 3. DF test
If you have a random walk, then it is not covariance stationary, and you cannot use an AR model to forecast. But, you can make it covariance stationary by doing a first differencing on it, then perform an AR(1) model regression. If the regression parameters and the autocorrelations are all insignificant, i.e., t-stats less than critical, then you know it is not covariance stationary, i.e., it is unit root. This is what I remember from this stuff, but I definitely need to go back and check.
To use AR(k) model, you use t-test=autocorrelation/std_error. std_error = 1/root_square(T-k) with df=T-k-1 (not sure about this, please confirm). Basically it starts from AR(1) till all Null hypotheses(for each lag) are rejected. Null hypothesis i: no autocorrelation for lag i. Never done it in real world, but I will learn SAS after June 7.