Answer: 1.0989

The unconditional variance of an AR(1) process is calculated using the formula: $$\text{Var}(y) = \frac{\sigma_u^2}{1 - \phi^2}$$ Where: - $\sigma_u^2$ is the variance of the disturbances (given as 1) - $\phi$ is the autoregressive coefficient (given as 0.3) Plugging in the values: $$\text{Var}(y) = \frac{1}{1 - (0.3)^2} = \frac{1}{1 - 0.09} = \frac{1}{0.91} \approx 1.0989$$ Note that the constant term (0.2) does not affect the variance calculation for an AR(1) process with zero-mean disturbances. The unconditional variance depends only on the disturbance variance and the autoregressive coefficient.

Author: Nikitesh Somanthe