Answer-first summary for fast verification
Answer: 0.69
The mean-reverting level for an AR(1) model is calculated as: $$\text{Mean-reverting level} = \frac{\text{intercept}}{1 - \text{AR parameter}}$$ Given: - Intercept = 0.24 - AR parameter = 0.65 Calculation: $$\text{Mean-reverting level} = \frac{0.24}{1 - 0.65} = \frac{0.24}{0.35} = 0.6857 \approx 0.69$$ This means that the time series tends to revert to a long-term mean of approximately 0.69. The AR(1) model specification is: $$Y_t = 0.24 + 0.65Y_{t-1} + \epsilon_t$$ For a stationary AR(1) process, the unconditional mean (mean-reverting level) is given by the formula above. Option A (0.69) is the correct answer.
Author: Nikitesh Somanthe
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An investment analyst wishes to forecast the future returns based on the prevailing interest rate then. The analyst chooses AR times series to model the monthly interest rates movement over 20 years. The equivalent AR(1) model has an intercept of 0.24 and an AR parameter of 0.65. What is the mean-reverting value of the times series used by the analyst?
A
0.69
B
0.56
C
0.65
D
0.54