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Estimate AR-Garch Model Parameters using garchfit and Arima

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George
George 2013-1-1
Hi everyone and happy new year
I am struggling to understand how to estimate the parameters of a AR-Garch model
I found on the documentation two ways which yields different results and i can't understand the difference
Below is my code:
%% Begin
clear all
clc
%% Load Variables
load data
load dates
%% Construct Variables
spotRates = data;
spotRets = [NaN(1, size(data,2)); price2ret(spotRates,[],'Periodic')];
%% First Way
model = arima('ARLags',[1 2 5 7], 'Variance',garch(1,1));
[fit,VarCov,LogL,info] = estimate(model,spotRets(2:end,1));
%% Second Way
arCoefs = cell2mat(fit.AR);
Spec = garchset('AR',arCoefs,'P',1,'Q',1);
% Here i used the coeffs from the arima estimate. I dont know how to set Lags 3 4 6
% equal to zero and the garchfit changes the AR coefficients that i gave
% Also i tried Spec = garchset('AR',arCoefs,'FixAR', [0 0 1 0 0 1 0], 'P',1,'Q',1);
% with the same results
[Coeff,Errors,LLF,Innovations,Sigmas,Summary] = garchfit(Spec,spotRets(2:end,1));
%% End
Also i can't understand the difference between the following
1) model = garch(1,1);
[fit,VarCov,LogL,info] = estimate(model, data)
and
2) spec = garchset('P',1,'Q',1);
[Coeff,Errors,LLF,Innovations,Sigmas,Summary] = garchfit(spec,data);
Also slightly different results Thank you very much for your time
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George
George 2013-1-1
Ok i found what is wrong
I forget to set the constant in the second way
If i give the following:
Spec = garchset('AR',cell2mat(fit.AR),'FixAR', [0 0 1 1 0 1 0], 'Constant', fit.C, 'P',1,'Q',1);
[Coeff,Errors,LLF,Innovations,Sigmas,Summary] = garchfit(Spec,spotRets(2:end,1));
the results are almost the same.
I have another question:
Does it matters whether the parameter 'AR' in the 'garchset' has the estimated coefficients?
I write
Spec = garchset('AR',[0.1 0.1 0 0 0.1 0 0.1], 'FixAR', [0 0 1 1 0 1 0], 'Constant', 0.1, 'P',1,'Q',1);
[Coeff,Errors,LLF,Innovations,Sigmas,Summary] = garchfit(Spec,spotRets(2:end,1));
and the results are the same
George
George 2013-1-1
I think that garchset/garchfit/garchsim/garchpred
and
garch/estimate/infer/simulate/forecast
produce the same results
I can't find the difference
Any help would be appreciated

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