- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 5. Time-Series Analysis
- Subject 3. Random Walks and Unit Roots
CFA Practice Question
What are correct characteristics of a random walk process (LOS h)?
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.
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.
Correct Answer: I and II
I is right as it does not have a finite mean. II is right as it does not have a finite variance.
III is wrong: If an AR(1) model has b0 = 0 and b1 = 1, it becomes a random walk time series.
IV is wrong: in this model, xt-1 is the best forecast of x in every period after t - 1.
User Contributed Comments 3
| 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. |