below is equation: R(t)=R(t-1)+e, is this a unit root or random walk, under which circumstance unit root is not random walk, if not unit root, can we say it will be covariance stationary. if coeeficient for R(t-1) t-test is 0.936 and test of significance is 0.95, can we reject H0 and model:R(T) is not unit root?(H0 should be model has unit root) which test we can use for seasonailty, how can find there is seasonality problem for model itself. should we use AR(4) or AR(12), what’s the cretia in choosing lag? can we use DW test for trend model’ s autocorrelation problem, but not for AR model, if for AR model, should we use T-test?
Your first equation is a random walk, which is a special type of unit root. If the coefficient is .936 then it is not a unit root by definition, using the b0 / (1-b1) equation. Depends on what data is presented. If quarterly, we use AR(4). If monthly, we use AR(12). DW test cannot be used on an AR model. You have to check if any of the lagged variables are statistically significant. If they are, then you have a problem.
bpdulog Wrote: ------------------------------------------------------- > Your first equation is a random walk, which is a > special type of unit root. > > If the coefficient is .936 then it is not a unit > root by definition, using the b0 / (1-b1) > equation. > > Depends on what data is presented. If quarterly, > we use AR(4). If monthly, we use AR(12). > > DW test cannot be used on an AR model. You have to > check if any of the lagged variables are > statistically significant. If they are, then you > have a problem. you’re on fire
The first equation is a random walk. The dependent variable is itself plus a random error. I believe unit root and random walk are basically descriptions of the same thing. A unit root is the description of the coefficient being equal to one. A random walk is more of a description of the trend.
Thanks, can you write a equation which is unit root but not random walk?, if a equation is not unit root, does it necessary to be cov, stationary? if coeeficient for R(t-1) t-test of coefficient is 1.2(given standard error 0.012, (0.987-1)/0.012=1.2, but test of significance is 0.3, although the equation is R(t)=0.987 R(t-1)+e, it is a unit root, because it significant statistically. DW test can be used in trend model. if given a model F(T)=12.3 F(t-1)+1.24 F(t-2)+23+E, without looking at the graph, how do you know to add lag(4) or lag(3), if T-test for lag 4 is 2.3(given 12.3/(SQUART(N))=2.3) and T-test for lag 3 is 3.3(given 32.3/(SQUART(N))=3.3) should we add lag 4 or lag 3 or both?
an equation has to be covariance stationary for it to be economically significant. DW test can be used in a trend model, but not in an AR(X) model. AR(X) model by definition is a model where data in one period depends on data in prior periods, and by that definition would definitely have serial correlation. in the last case - you would first add the last significant T-stat - in this case 4. then check the new model autocorrelations again. at that point all of the autocorrelations should have become insignificant.
Thanks why can’t add lag3, the book says all T-test significance should be add to the model. should we use first differencing to correct auto-correlation in AR model and use T-test for checking auto-correction in AR model or should we use Dicky fuller test ? Is Dicky fuller test same as Dicky fuller EG test which is used for cov. stationary?
you would first add 4. If after that on the test of the autocorr. you find 3 is still significant, add it later. You would not add all at one shot. It is an iterative process.
Thanks, I will use that idea. can you eleaborate more on using first differencing technique and Dicky fuller test for AR model?
Dickey Fuller is used to test for a unit root. If a unit root exists, use Dickey Fuller Engle Granger T-test statistics to test for cointegration. If both sets of data (dependent var and independent var) are cointegrated, proceed. If one is, and the other is not, your model is misspecified, don’t proceed. If no cointegration in either, proceed. Dude, this is all pretty understandable. A random walk always does not exhibit covariance stationarity…that’s why you first difference it. (you need a constant mean and variance) Don’t forget random walks with drift, where b0 = 1. If you want to see if something is cov stat, plot it, or look for the Mean Reverting Level, which is given above as b0/1-b1 Cheers…