# What does a first-differenced model tell you?

You try to use an AR(1) model, but then realize it is not covariance stationary because it is a random walk. X(t) = X(t-1) + E To fix this, you first difference the model, so it is mean reverting to zero. Y = X(t) - X(t-1) = E What does this new model tell you? I can’t figure out how it is an improvement on the old model except the CFAI says it is. Thanks!

Now it’s covariance stationary… Since Y(T) = 0 + 0 x Y(T-1) + E Mean reverting level is: 0/0 = 0 This means the best prediction of the next period value is this period value.

its solves dickey’s unit problem.

lxwqh Wrote: ------------------------------------------------------- > Now it’s covariance stationary… > > Since Y(T) = 0 + 0 x Y(T-1) + E > > Mean reverting level is: 0/0 = 0 > > This means the best prediction of the next period > value is this period value. OK I think I got it now. The model after first differencing doesn’t really tell you anything new… that’s my problem. I.E. you run the dickey fuller test, so you know the model is a random walk. So you’ve established that already, then you first difference the model only to discover that the best prediction of the next period is this period value. BUT you knew that already from the results of the DF test. Oh well, probably just over-thinking it.