Is there closed-form solution for mean absolute deviation (MAD) for AR(1) process?
$X_t = c + \beta X_{t-1} + \epsilon_t $
$\epsilon_t \sim N(0,\sigma^{\epsilon})$
(Similar to the variance and the mean for AR(1): as we can derive mean as $\frac{c}{1-\beta}$ and variance as $\frac{\sigma_t^{epsilon}}{1-\beta}$.)
But for MAD how to proceed from this? Or there's no closed-form solution?
$$MAD = |X_t - E[X_t]| = |c + \beta X_{t-1} + \epsilon_t - \mu|,$$
where $\mu = E[X_t]$.
