GARCH significance, what is the precise number?

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?

Answer 1

[Wayne King]

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.

Answer 2

[Wayne King]

Sorry, I may have misinterpreted your original question. If you are talking about the output of garchfit:

 Parameter       Value          Error       T Statistic 
 -----------   -----------   ------------   -----------
           C    -0.0013526     0.0013368       -1.0119
           K    0.00027647     0.00014944       1.8500
    GARCH(1)    0.77871        0.10106          7.7057
     ARCH(1)    0.073557       0.028595         2.5724

Then the T-statistic is Value/Error, so how many standard errors is the Value away from the null value of zero. You can use a t-statistic of 2 as an indication of 0.05 significance in this instance.

[Yoshiko Kawashima]

right that is what I meant. So if the T Statistics is bigger than 2 then it is significant. is that correct?

[amine guiri]

I HAVE THE SAME QUESTION , it's is significant if it's bigger than 2 FOR 0.05 ?