FRM Part I · FRM Exam Part I · Nonstationary Time Series
A quarterly series is modeled as Y_t = 50 + 0.5t + 8·Q2_t + 3·Q3_t − 12·Q4_t + e_t, where Q1 is the base quarter and t = 1 in the first quarter of year 1. What is the forecast for the fourth quarter of year 3 (t = 12)?
The forecast is 44. The intercept plus trend gives 50 + 0.5×12 = 56, and the fourth-quarter seasonal coefficient of −12 is added, producing 44. Ignoring the seasonal dummy gives 56, and flipping its sign gives 68, both incorrect.
- A44Correct
- B56
- C68
- D44.5
Explanation
Trend: 50 + 0.5×12 = 56. The Q4 dummy adds −12, giving 56 − 12 = 44. Distractor 56 ignores the seasonal term; 68 uses the wrong sign on the Q4 coefficient.
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