Answer-first summary for fast verification
Answer: [-0.0645, 0.0695]
The 95% confidence interval is given by: $$ E_T(Y_{T+h}) \pm 1.96\sigma $$ We need: $$ E_T(I_3) \pm 1.96\sigma $$ First, calculate the expected value: $$ E_T(Y_{T+h}) = \sigma_0 + \sigma_1(T + h) $$ $$ = -0.001567 + 0.000134 \times 3 = 0.0025 $$ Then calculate the confidence interval: $$ E_T(I_3) \pm 1.96\sigma = 0.0025 \pm 1.96 \times 0.0342 $$ $$ = 0.0025 \pm 0.067032 $$ $$ = [-0.064532, 0.069532] \approx [-0.0645, 0.0695] $$ Therefore, the 95% confidence interval for interest rate movement 3 years from now is [-0.0645, 0.0695].
Author: Nikitesh Somanthe
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A log-linear trend model is approximated on the interest rate (in %) movement in a certain market given as:
for the last 20 years. The standard deviation of the residual is 0.0342. Assuming that the residuals are white noise, what is the 95% confidence interval for interest rate movement 3 years from now.
A
[0.9517, 0.6257]
B
[-0.6917, 0.8259]
C
[-0.0645, 0.0695]
D
[0.7917, -0.6917]