Hi,
I'm trying to stimate the power ewma volatility (Guermat and Harris, 2002).
I would like to use it for VaR stimation.
The difference of "Ewma" and "power Ewma" is that the latter assumes
Generalized error distribution (GED). The power Ewma estimator is based on
the maximum likehood of the variance of exponential power
distribution.Conditional on the power parameter (omega), calculated from
the probability density function of GED, the maximum estimator of the
standard deviation of power exponential distribution is:
sigma(t+1)^omega= lambda*sigma(t)^omega+(1-lambda)*g(omega)*abs(Rt)^k.
where K=kurtosis e g(omega)=omega*standar gamma
function(3/omega)^(omega/2)*standard gamma function(1/omega)^-omega/2
so, I sould:
1. calculate omega with maxLik for a series of log return using the formula
above which depends on k
If anybody knows how to solve it with R?
Thanks a lot
Jo
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