likelihood ratio test and GARCH models

[marwa]

Dear all,
I am working on different types of GARCH models like the simple GARCH (1,1), GARCH in mean, Threshold GARCH, and exponential GARCH models. How can I compare among them using the Likelihood Ratio test, I have eviews 6 and I can't find a command for likelihood ratio, it is only available in the test for omitted or redundant variables, but then I am using the same set of explanatory variables in all equations the only difference is the use of the garch in the mean equation or the threshold in the variance equation.
Also can I create a big model to include the GARCH variable in the mean and the threshold variable in the variance equation, to be my nested model, and then compare it to the other individual GARCH models. IF yes, can I use the likelihood ratio test to do this, can you please tell me how?
If no, do you have any suggestions in how to compare different GARCH type models?
Thank you

[doaa]

Hello, I think it is very late reply and may be you do not need it now but may be others can benefit from the answer. One thing you could do is to make a programme includes these different types of models and by the end you write a command for running a likelihood ratio test. You mentioned that you want to compare between simple GARCH(1,1), GARCH-M, TARCH, and EGARCH. Given that the variable you want to model is Y and you want to regress it on a constant and its first lag (just for simplicity ) where your data is saved in a file named "data" (of course you can change the file name and the sample that fits you) .
The programme may be written as follows
'change path to program path
%path = @runpath
cd %path

' load workfile
load data
'set sample
sample s0 1957:2 2007:2

' estimate GARCH(1,1) model
equation eq1.arch(1,1) y c y(-1)
show eq1.output

' estimate GARCH(1,1)-M model
equation eq2.arch(1,1, archm=var) y c y(-1)
show eq2.output

' estimate TARCH(1,1,1) model
equation eq3.arch(1,1, TTHRSH=1) y c y(-1)
show eq3.output

' estimate EGARCH(1,1,1) model
equation eq4.arch(1,1, ASY=1,EGARCH) y c y(-1)
show eq4.output

' LR statistic to compare different models
scalar lr = -2*( eq1.@logl - eq2.@logl )
scalar lr_pval = 1 - @cchisq(lr,q)

' where q is the difference of the parametrs estimated between the constrained and unconstrained model. In this regard, I assumed that the unconstrained is eq1. you can change the calculation of LR depending on which is the constrained.


Another way to do this is to estimate the four different models as usual, then in the command bar type in the command of calculating LR as follows
scalar lr = -2*( eq1.@logl - eq2.@logl )
scalar lr_pval = 1 - @cchisq(lr,q)


Good Luck :D
Doaa

[KimFong]

how to different constrained and unconstrained eq,?
i try it, yet it needs to defined q first.
please show me, thanks.

[doaa]

Hi
Computing LR test between GARCH(1,1) and GARCH(1,1)-M is as follows
The constrained version of the model is GARCH(1,1) (eq1 in the programme of my previous post) as it assumes that the coefficient of GARCH-in-mean is zero, and of course the unconstrained equation is GARCH-M (equation 2)
To define the number of restriction q is very simple, here q=1 as we just impose one restriction on the GARCH-in-mean parameter.

Good luck

[KimFong]

Thank You Doaa, I so stressful with my academic writing. Thanks God.
You helped me in time... :D

[doaa]

You are always welcome.
Good luck with your academic writing :D