- CFA Exams
- CFA Exam: Level II 2021
- Study Session 2. Quantitative Methods (1)
- Reading 6. Time-Series Analysis
- Subject 4. Seasonality in time-series models

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**CFA Practice Question**

An analyst decides to use the following equation to model quarterly sales of company X.

1 | -0.1699 | -0.2531

2 | -0.0913 | -2.74

3 | -0.1922 | 0.7893

4 | 0.3214 | 3.2132

B. One seasonal lag should be added to the AR model.

C. Two seasonal lags should be added to the AR model.

ln Sales

_{t}- lnSales_{t-1}= b_{0}+ b_{1}(ln Sales_{t-1}- lnSales_{t-2})+ ε_{t}Here are autocorrelations of the residual.

Lag | Autocorrelation | t-Statistic

1 | -0.1699 | -0.2531

2 | -0.0913 | -2.74

3 | -0.1922 | 0.7893

4 | 0.3214 | 3.2132

The critical value for a t-statistic is about 2.0 at the 0.05 significance level. What would you recommend based on the regression result?

A. The model is correctly specified.

B. One seasonal lag should be added to the AR model.

C. Two seasonal lags should be added to the AR model.

Correct Answer: C

The null hypothesis that the second and the fourth autocorrelations are equal to 0 can be rejected.

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**User Contributed Comments**
4

User |
Comment |
---|---|

noonah |
what is the argument against A, the model is correctly specified? |

gkobylko |
In the text book examples, even when there are more then one statistical significant autocorrelation of residuals, it adds only one (the most significant) seasonal lag to the AR model. Which one is corret, the CFA text book or the analyst notes method? |

nike |
In the textbook example there is only one value that's bigger than 2.0 (critical value). That's the fourth quarter. Here in this example there are two values (the second and the fourth quarter). So the question is correct. |

ericczhang |
The model is not correctly specified because it only models one seasonal lag in the first previous quarter. |