MATLAB: GARCH significance, what is the precise number

garchsignifinace

When performing GARCH, EGARCH and JRR Matlab produces : Value-Standard Error and t-stat. how do we find out if the t-stat is significant e.g. should it be very big or small and what is the precise number for 5% significance.I exactly need to know how they call something significance?

Best Answer

Hi, You have to evaluate the t-statistic on the appropriate t-distribution. The t-distribution is characterized by one parameter, the degrees of freedom. So for example, in the following GARCH model, the degrees of freedom are 8.
model = garch('Constant',0.0001,'Garch',0.75,...
         'Arch',0.1,'Offset',0.5,'Distribution',struct('Name','t','DoF',8));
You can use tcdf() and tinv() to evaluate significance. If you wanted only 0.05 of the probability outside that number in a two-tailed test.
dof = 8;
tlow = tinv(0.05/2,dof);
thigh = tinv(1-(0.05/2),dof);
Gives you your upper and lower critical values. The t-distribution is symmetric around zero, so they differ only in sign.
If you observed a t-statistic of 2.5, to find the p-value
2*(1-tcdf(2.5,dof))
The above is for a two-tailed test of significance.
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