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.