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st: estimating time-varying betas and variance of error terms


From   Kuncho Tsilkov <kuncho_bg@yahoo.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: estimating time-varying betas and variance of error terms
Date   Sun, 11 Dec 2011 04:29:31 -0800 (PST)

hi all,
 
Is there a code that would allow me to estimate the time varying "betas" and variance of the residuals from the first equation,
for the computation of the PV measure. I have already esitmated the residuals and I run a GARCH model which is shown in the first equation.
 
I have the following model where R denotes returns:
R(x,t) = α0 + a1 R(x,t-1) + (β0 + β1*D2005 + β2*D2008) ε(y,t) + (γ0 + γ1*D2005 + γ2*D2008) ε(z,t) + (δ0 + δ1*D2005 + δ2*D2008) ε(w,t) + ε(x,t)      
 
I want to calculate the proportion of variance that is accounted for by each of the factors, in the above equation, in the following manner:
PV(y,t)= [(β(y,t)^2) * Var(ε(y,t))] / [(β(y,t)^2) * Var(ε(y,t)) + (β(z,t)^2) * Var(ε(z,t)) + (β(w,t)^2) * Var(ε(w,t)) + h(x,t)]

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