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Basic Question 3 of 6

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

ln Salest - lnSalest-1 = b0 + b1 (ln Salest-1 - lnSalest-2)+ εt

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.
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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.
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I am happy to say that I passed! Your study notes certainly helped prepare me for what was the most difficult exam I had ever taken.
Andrea Schildbach

Andrea Schildbach

Learning Outcome Statements

explain how to test and correct for seasonality in a time-series model and calculate and interpret a forecasted value using an AR model with a seasonal lag;

CFA® 2025 Level II Curriculum, Volume 1, Module 5.