Answer: 0.69

## Explanation For an AR(1) model of the form: $$Y_t = c + \phi Y_{t-1} + \epsilon_t$$ Where: - c = intercept = 0.24 - φ = AR parameter = 0.65 - ε_t = white noise error term The mean-reverting level (long-term mean) of the time series is calculated as: $$\text{Mean-reverting level} = \frac{c}{1 - \phi}$$ Substituting the given values: $$\text{Mean-reverting level} = \frac{0.24}{1 - 0.65} = \frac{0.24}{0.35} = 0.6857$$ This means the time series will tend to revert to approximately 0.69 over the long term. **Key Points:** - The mean-reverting level represents the long-term equilibrium value that the time series tends to approach - For an AR(1) model, this is calculated as intercept divided by (1 - AR parameter) - The result 0.6857 rounds to 0.69, which matches option A - This calculation assumes the time series is stationary (|φ| < 1)

Author: Tanishq Prabhu