Answer-first summary for fast verification
Answer: [12.030, 13.754]
## Explanation For a log-linear model with normally distributed residuals, the 95% confidence interval for the forecast is calculated using: 1. **Expected value of ln(Y_T)**: $$\mathrm{E}_T[\ln Y_T] = -0.1567 + 0.00134 \times 2023 = 2.554$$ 2. **Variance adjustment**: $$\frac{\sigma^2}{2} = \frac{0.0342^2}{2} = 0.0006$$ 3. **Expected value of Y_T**: $$\mathrm{E}[Y_{2023}] = \exp(2.554 + 0.0006) = 12.866$$ 4. **Error bounds multiplier**: $$\exp(\pm 1.96 \times 0.0342) = [0.935, 1.069]$$ 5. **95% Confidence Interval**: $$95\%\text{CI}_{2023} = [0.935 \times 12.866, 1.069 \times 12.866] = [12.030, 13.754]$$ This approach accounts for the log-normal distribution properties and provides the correct confidence interval for the interest rate forecast.
Author: Tanishq Prabhu
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A log trend model is approximated on the interest rate (in %) movement in a certain market based on data from 2000 until 2020. The estimated model is given as:
The standard deviation of the residual is 0.0342. Assuming that the residuals are normally distributed, what is the 95% confidence interval for interest rate movement for year 2023?
A
[12.030, 13.754]
B
[12.018, 13.739]
C
[-0.0584, 0.0756]
D
[11.994, 13.713]
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