FRM Part I · FRM Exam Part I · Stationary Time Series
Quarterly sales of a firm are modeled by regressing on quarterly dummy variables (Q1 as the omitted base) with an intercept: Sales = 80 + 5*D2 + 20*D3 + 35*D4 + error, in USD millions. What is the model's expected sales for the third quarter, and how much higher is expected fourth-quarter sales than expected second-quarter sales?
Third-quarter expected sales equal the intercept plus the Q3 coefficient: 80 + 20 = 100 million. Q2 is 85 and Q4 is 115, so Q4 exceeds Q2 by 30 million. Dummy coefficients measure differences from the omitted base quarter, Q1.
- AQ3 = 20; Q4 higher than Q2 by 30
- BQ3 = 100; Q4 higher than Q2 by 15
- CQ3 = 100; Q4 higher than Q2 by 30Correct
- DQ3 = 120; Q4 higher than Q2 by 35
Explanation
Q3 expected sales = 80 + 20 = 100. Q2 = 80 + 5 = 85 and Q4 = 80 + 35 = 115, so the difference is 115 - 85 = 30. The option giving 15 mistakenly uses 20 - 5 (Q3 minus Q2).
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