If the time series has a unit root ie b is equal 1, does the series exhibit random walk? What does actually random walk mean? Is it a misspecification of the model?
Hi Mike,
When B = 1 the series has a unit root and we call this type of non-stationary series as a series that follow a random walk process. When a series has a unit root the series is non-stationary and cannot use the model to forecast. In order to transform a series having a unit root into a stationary one, you have to difference it. The number of times you difference indicate the order of the series.
Also when a series has a unit root the assumptions of stationary do not longer hold.
Dont forget to differente between random walk and random walk with drift.
Hope this helps.
Hi Chrisglo, many thanks for the explanation. My understanding is that both random walk and random walk with a drift (ie intercept) are non-covariance stationary.
This is incorrect. The order of the series is indicated by the number of lags used as explanatory (independent) variables. For the purposes of the curriculum you won’t have to use higher order differences.
Hi Panos,
The order you are referring to are for AR and MA or ARMA models. What I referred to, was order of integration when differencing. When differencing once, it is integrated of order 1, differencing two order 2 and if it is already stationary it will be of order zero.
Sorry for any misunderstanding.
Hey Chris,
I was just clarifying to avoid confusion to future readers! The curriculum only refers to the order of the AR,MA & ARMA models as indicated by the lags used to specify them. The order of integration becomes relevant after we move higher than first order differences and is not touched upon in the curriculum.