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questions on garch math:
1. does anyone have the original Bollerslev's 1986 or 1994 garch paper?
i would appreciate a copy.
2. is there a garch user group somewhere out there?
3. does anyone have a paper on garch mle estimation, in particular the
derivation of the log likelihood function by recursive substitution of the
variance term in the model, sometimes called the derivation in form of arma innovations?
4. more details on previous question. if no paper comes through
could someone then help on the derivation
of the garch model by the recursive substitution part?
the general model is ( i substituted sigma with V and removed squared )
Vt = a + b*Vt-1 + c*Et-1
as you might notice that Vt is a function of Vt-1 meaning it's recursive ie
Vt-1 itself = a + b*Vt-2 + c*Et-2 and so on
question: need to rewrite the equation by recursively substituting
Vt -n with Et-n term so that the loglikelihood function is only a function of
innovations c*Et and LnL can be derived easier.
all the reference papers i got on garch either skip the derivation or
do not provide the end form loglikelihood function... either it is too simple
or nobody bothers since it was done already and hard coded in the garch packages.
could someone walk me through it please or point to a paper, just the rewriting by
recursive substitution part, not the LnL derivation( ( that i know)?
***from the math point of view,
last question is basically math question, as you can disregard the above garch notion...
pure math problem is:
(1) Yt = a + b*Yt-1 + c*Xt-1
need to rewrite 1 so that Yt = f( a,b,c Xt-1) only, no Yt-n in there.
thanks.
bilo.
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