# Thread: Is AR(1)-ARCH(1) covariance stationary?

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

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 .
I also know that an ARCH(1) is covariance stationary if and .

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

2. ## Re: Is AR(1)-ARCH(1) covariance stationary?

Yes, in the unconditional sense.

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