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**Basic Question 1 of 5**

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.###
**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. |

I used your notes and passed ... highly recommended!

#### Lauren

**Learning Outcome Statements**

explain the instability of coefficients of time-series models;

describe characteristics of random walk processes and contrast them to covariance stationary processes;

describe implications of unit roots for time-series analysis, explain when unit roots are likely to occur and how to test for them, and demonstrate how a time series with a unit root can be transformed so it can be analyzed with an AR model;

*CFA® 2024 Level II Curriculum, Volume 1, Module 5.*