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?