FRM Part I · FRM Exam Part I · Nonstationary Time Series
A log-linear trend model for annual earnings is estimated as ln(Y_t) = 3.00 + 0.05 t. The model predicts earnings at t = 10. Using the exact exponential (ignoring any variance adjustment), what is the predicted level of earnings, to the nearest whole number? (Use e^3.5 = 33.12.)
Predicted earnings are about 33. The log forecast is 3.00 + 0.05 × 10 = 3.50, and exponentiating gives e^3.5 ≈ 33.12. The value 3.5 is the log of earnings, not the level.
- A20
- B33Correct
- C35
- D3.5
Explanation
ln(Y) = 3.00 + 0.05 × 10 = 3.50. Y = e^3.5 = 33.12, about 33. Reporting 3.5 leaves the answer in logs. Choosing 35 would incorrectly treat the result as 3.5 × 10, and 20 approximates e^3.
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