TGARCH variance

Besnik

2012 5 24

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Hi I have estimate the conditional variance of a given financial time series data under the hypothesis that the returns follow a student t distribution with this specification

spec = garchset('P',1,'Q',1,'C',NaN,'Distribution','T','Display','off'); 
h=par.K + par.ARCH+par.GARCH;

I want this to estimate the Value at Risk. What I wanna know is if the variance estimated with this code is corrected by the degrees of freedom (I have set the degrees of freedom 10).I can't find in any manual how this variance is estimated and if is corrected by the degrees of freedom! Thank you very much.

EDIT [25 May 2012, 13:36 BST - OK] Added code from comments.

T=length(r); WE=1000;
p = 0.01;
VaR = zeros(T,1);
spec = garchset('P',1,'Q',1,'C',NaN,'Distribution','T','Display','off');
for t=WE+1:T
    t1 = t-WE; t2 =t-1;
    window = r(t1:t2);
    [par, errors, LLF, innovations, ht]=garchfit(spec,window);
    h=par.K + par.ARCH*window(end)^2+par.GARCH*ht(end)^2;
    VaR(t,1)=-sqrt(h)*tinv(p,10);
end

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Oleg Komarov 2012-5-24

I think you skipped some lines of code, where does 'par' come from?

Besnik 2012-5-25

Hi the code is

T=length(r); WE=1000; p = 0.01: VaR = zeros(T,1); spec = garchset('P',1,'Q',1,'C',NaN,'Distribution','T','Display','off'); for t=WE+1:T t1 = t-WE; t2 =t-1; window = r(t1:t2); [par, errors, LLF, innovations, ht]=garchfit(spec,window); h=par.K + par.ARCH*window(end)^2+par.GARCH*ht(end)^2; VaR(t,1)=-sqrt(h)*tinv(p,10); end

with this code I estimate the parameters and calculate the variance under the hypothesis that the returns follow a student t distribution. par is for parameter. What I want to know is if the variance calculated in this way is corrected by the degrees of freedom this is very important for my thesis. Thank you.

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