Is AR(1)-ARCH(1) covariance stationary?

A_Jo

New Member
I'm becoming confused by this. Say I have the following model:

$y_t = c + \phi y_{t-1} + \epsilon_t, \epsilon_{t}|\Omega_{t-1} ~ \textasciitilde{} ~ WN(0,\sigma^2_t)$

$\sigma^2_t = \alpha_0 + \alpha_1 + \epsilon^2_{t-1}$

$\sigma^2_t = \alpha_0 + \alpha_1 + \epsilon^2_{t-1}$

I know that an AR(1) is covariance stationary if [TEX]|\phi|<1[/TEX].
I also know that an ARCH(1) is covariance stationary if [TEX]\alpha_0, \alpha_1>0[/TEX] and [TEX]\alpha_1<1 [/TEX].

If those conditions hold does that imply that an AR(1)-ARCH(1) is also covariance stationary?