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GARCH with alpha-stable residuals
Posted: October 11th, 2010, 7:50 pm
by maratikus
I am trying to estimate parameters of ARMA(1,1)-GARCH(1,1) model when residuals have alpha-stable distribution. I would appreciate if someone could point me in the right direction.
GARCH with alpha-stable residuals
Posted: October 12th, 2010, 9:41 am
by eh
I would have thought that a maximum likelihood estimation (MLE) would work.
GARCH with alpha-stable residuals
Posted: October 12th, 2010, 12:34 pm
by maratikus
QuoteOriginally posted by: ehI would have thought that a maximum likelihood estimation (MLE) would work.I would be happy to use MLE but the question is how to implement it for alpha-stable case. I haven't seen that anywhere.
GARCH with alpha-stable residuals
Posted: October 12th, 2010, 2:30 pm
by eh
Instead of using the Gaussian likelihood, you will need to use the alpha stable likelihood. I guess the easiest way to calculate the alpha stable likelihood is through Fourier inversion of the characteristic function.