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### Basic Question 1 of 5

What are correct characteristics of a random walk process (LOS h)?

I. It is not mean-reverting.
II. It is not covariance-stationary.
III. If an AR(1) model has b0 = 1 and b1 = 0, it becomes a random walk time series.
IV. There is no best forecast of xt that can be made in period t - 1 since the value of xt is random.

User Comment
MasterD 1) A random walk is a special case of AR(1) where B0 = 0 and B1 = 1 (not as in III). Thus the mean reverting level = B0/(1-B1) = 0/0 and thus undefined. The textbook does state that "Therefore, a first-differenced random walk has a mean-reverting level of 0."
nsmwaura A random walk is where the predicted value of a series inn one period is equal to the value of the seris in the previous period plus a random error term.
nsmwaura B0 can be=0 if its random walk without a drift or not=0 if its a random walk with a drift. Eitherway, the meanreverting level will be undefined.