Dear BUGS users.
We are trying to estimate the following CAPM model using BUGS:
The observational equation is
Rp(t) = beta(t)*Rm(t) + sigma_p
Rp and Rm are observed while beta is unobserved.
And the state equation is
beta(t) = alpha - delta*[beta(t-1)-alpha] + sigma_b
In this model the alpha is the long-term mean and delta is the persistence
away from this long-term mean of beta. Our numbers are very stable but
biased. Can anyone see any errors in our model or even have some suggestions
that may improve it? You will find our model below.
model;
{
# N equals number of portfolios, while T equals number of periods.
for (n in 1 : N)
{
beta[n,1]<-1
alpha[n] ~ dnorm(meanalpha[n],vara[n])
delta[n] ~ dnorm(meandelta[n],vard[n])I(-1,1)
meanalpha[n] ~ dnorm(1,10)
meandelta[n] ~ dnorm( 0.5,10)
varb[n] ~ dgamma(0.001,0.001)
sigmab[n] <- 1 / sqrt(varb[n])
varr[n] ~ dgamma(0.001,0.001)
sigmar[n] <- 1 / sqrt(varr[n])
vara[n] ~ dgamma(0.001,0.001)
vard[n] ~ dgamma(0.001,0.001)
# observation model.
for( i in 1 : T )
{
rp[n,i] ~ dnorm(marketfactor[n,i],varr[n])
marketfactor[n,i] <- beta[n,i] * rm[i]
}
# state model.
for (i in 2 : T) {
beta[n,i] ~ dnorm(meanbeta[n,i],varb[n])
meanbeta[n,i] <- alpha[n] + delta[n] * (beta[n,i-1] - alpha[n])
}
}
}
Yours truly
Per Thorkildsen
Erik Smith-Meyer
Post-grad students at Norwegian School of Management
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