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FRM Part I · FRM Exam Part I · Stationary Time Series

Quarterly sales of a retailer are modeled with a deterministic seasonal regression using an intercept and three quarterly dummies (Q2, Q3, Q4), with Q1 as the base. Estimated coefficients: intercept = 120, Q2 = 15, Q3 = -10, Q4 = 45. What is the model's expected sales for Q4 and what does the Q3 coefficient represent?

Expected Q4 sales are 165, the intercept of 120 plus the Q4 coefficient of 45. The Q3 coefficient of -10 means Q3 sales average 10 below the omitted base quarter, Q1, not below the annual average.

  1. A165; Q3 sales are 10 below Q1 sales on averageCorrect
  2. B165; Q3 sales are 10 below the annual average
  3. C45; Q3 sales are 10 below Q1 sales on average
  4. D110; Q3 sales are 10 below the Q4 level

Explanation

Expected Q4 = intercept + Q4 coefficient = 120 + 45 = 165. Each dummy coefficient measures the difference from the omitted base quarter (Q1), so -10 means Q3 is 10 below Q1. Interpreting it relative to the annual average is wrong because the base is Q1.

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