Barra seems to use the following model for specific asset risk from page 67-68 of this guide to factor models: www.cfapubs.org/doi/pdf/10.2470/rf.v1994.n4.4445:
$\mu^2(t)$ = S(t) [ 1 + v(t) ]
where S(t) = average specific variance across the universe of stocks and v = cross-sectional variation in specific variance
Can anyone explain why they use this to model specific asset risk vs. say GARCH(1,1) and what the differences would be? There seems to be very little written on their specific asset risk model.