Thanks for the package. No, I didn't check the log likelyhoods of TimeSeriesModelFit or EstimatedProcess - simply because I don't know how to! Could you point me in the right direction?

Hi Milos,

Thanks for the mathematica code and notebook. One quick question: do you know why your algorithm returns different parameters to the GarchProcess function in Mathematica 10.x? Which one is correct in your opinion?

Hi Sandu,here is my first code that uses Memorization

garch[s_] := Module[{k = s, R, \[Sigma]sqr, ll, sll, u},
  k = Flatten@k;
  R[t_] := Flatten[k][[t]];
  \[Sigma]sqr[1, w_, a_, b_] := Variance[Flatten[k]];
  \[Sigma]sqr[t_, w_?NumberQ, a_?NumberQ, 
    b_?NumberQ] := \[Sigma]sqr[t, w, a, b] = 
    w + a R[t - 1]^2 + b \[Sigma]sqr[t - 1, w, a, b];
  ll[t_, w_?NumberQ, a_?NumberQ, b_?NumberQ] := 
   ll[t, w, a, b] = 
    If[\[Sigma]sqr[t, w, a, b] > 
      0, -.5 (Log[2 \[Pi]] + Log[\[Sigma]sqr[t, w, a, b]] + 
        R[t]^2/\[Sigma]sqr[t, w, a, b]), -1000]; 
  sll = Sum[ll[t, w, a, b], {t, 2, k // Length}];
  u = NMaximize[{sll, a > 0, b > 0, w > 0, a + b < 1}, {w, a, b}, 
    WorkingPrecision -> 12, MaxIterations -> 100];
  Print[u];
  Remove[k];
  Remove[R];
  Remove[\[Sigma]sqr];
  Remove[ll];
  Remove[sll];
  ClearAll[k, R, \[Sigma]sqr, ll, sll, u];]

I used If function to avoid numerical obstacles of imaginary numbers (log(negative value) may occur) as in Christoffersen book. This is Garch with normal innovation but you can always change log likelihood. Unfortunately this is still kinda slow so after some time i found a new way, I wont post the code here, instead I'll attach a notebook with code.It is pretty fast and If you want your function to be entirely in Mathematica it will do.The problem for me was (as will be for you) the mathematica optimizer, it didn't always converge and it needs tuning( WorkingPrecision and MaxIterations) in order to give satisfying result (I use default algorithm Neldear Mead). And finally If you give me your mail I'll send you my package with installation instructions, it has functions for univariate and multivariate garch estimation and it took me a lot of time to develop it.Please contact me on this post if you have any questions.

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It's something I'm wondering about too.I don't know the answer to that question but I can provide you with code so you can do Garch parameter estimation yourself.This is something I've been tackling for the past few months.Finally I created a package that does exactly that it's based on R functions and RLink.Basically if you want to for example estimate Garch(1,3) model with Student cond. distribution the command in package would be:

Ugarch[data,"garch(1,3)","coef",ConditionalDistribution->"StudentTDistribution"]

For Generalized error :

Ugarch[data,"garch(1,3)","coef",ConditionalDistribution->"Erf"]

For Skewed Student:

Ugarch[data,"garch(1,3)","coef",ConditionalDistribution->"SkewStudentTDistribution"]

,and so on.Interested??