- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 6. Time-Series Analysis
- Subject 3. Random Walks and Unit Roots

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**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 b

IV. There is no best forecast of x

I. It is not mean-reverting.

II. It is not covariance-stationary.

III. If an AR(1) model has b

_{0}= 1 and b_{1}= 0, it becomes a random walk time series.IV. There is no best forecast of x

_{t}that can be made in period t - 1 since the value of x_{t}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 b

_{0}= 0 and b_{1}= 1, it becomes a random walk time series.IV is wrong: in this model, x

_{t-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. |