Hi,
I am trying to find the conditional variance for multiple countries' HP filter ln of GDP using the following model:

Yit = ci + ε

where εit ~ N(0,hit)

hit = wi +αε2it-1 + βhit-1

Where Y is the lnGDP, c is a constant and h is the conditional variance.

Currently, my command used is: 'arch austria, arch(1/1) garch(1/1)' where Y=austria in this example.

I am unsure whether the GARCH models the conditional variance as stated in the third equation or whether I am supposed to specify this equation myself. I would greatly appreciate if someone could clarify this, I am basing my research off this paper which provides more detail if anything was unclear in my post
http://ec.europa.eu/economy_finance/.../ecp402_en.pdf