FRM Part I · FRM Exam Part I · Nonstationary Time Series
A log-linear trend model is estimated as ln(y_t) = 4.0 + 0.02t. What is the forecast of y at t = 50, closest to?
The forecast is about 148.4. The model predicts the log value 4.0 + 0.02×50 = 5.0, and exponentiating that gives e^5, approximately 148.4. Forgetting to convert back from logs would incorrectly give 5.0.
- Ae^5.0 ≈ 148.4Correct
- Be^4.02 ≈ 55.7
- Ce^5.0 × 50 ≈ 7,420
- D5.0
Explanation
Compute ln(y_50) = 4.0 + 0.02 × 50 = 5.0. Exponentiate: y = e^5.0 ≈ 148.4. Reporting 5.0 forgets to reverse the log, and the others use wrong arithmetic.
Did you get it right without looking?
One question tells you little. A timed set on Nonstationary Time Series shows your real accuracy, how long you take and where you lose marks.
More Nonstationary Time Series questions
- A quadratic trend model for annual output is y_t = 100 + 6t - 0.1t^2 + e_t. At which value of t does the fitted trend reach its maximum, and…
- An analyst models monthly sales of a firm with the linear trend model y_t = 50 + 2.5t + e_t, where t = 1 in the first month of the sample. B…
- Two series X_t and Y_t are each I(1). An analyst regresses Y_t on X_t in levels and tests the residuals with an Engle-Granger procedure, rej…
- In a Dickey-Fuller regression ΔY_t = δ + γY_{t-1} + ε_t on 250 observations of a bond yield, the estimate of γ is -0.040 with a standard err…
- An analyst fits y_t = 0.4 + 1.0 y_{t-1} + e_t with sigma² = 0.09 to a price series that starts at y_0 = 50. Using the model, what are the ex…
- An analyst models the log of a stock index level as y_t = 0.002 + y_{t-1} + e_t, where e_t is white noise with variance 0.0004. Which descri…