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

[A_Jo]

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

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?

 

[staassis]

Yes, in the unconditional sense.