## GARCH with an ARMA mean equation

Discussions of ARCH, GARCH, and related models

### GARCH with an ARMA mean equation

Hi there, I am new at RATS, just picked it up two days ago so my question might be naive.

I am trying to estimate a GJR GARCH model with an ARMA structure in the mean equation. I am using the FRML command, but I get an error message that FRML cannot handle MA terms:

## NL4. FRMLs Cannot Have Moving Average Parameters

Is there a way around this? Thanks in advance.
Nai_re_PAOK

Posts: 3
Joined: Thu Mar 31, 2011 10:24 am

### Re: GARCH with an ARMA mean equation

Nai_re_PAOK wrote:Hi there, I am new at RATS, just picked it up two days ago so my question might be naive.

I am trying to estimate a GJR GARCH model with an ARMA structure in the mean equation. I am using the FRML command, but I get an error message that FRML cannot handle MA terms:

## NL4. FRMLs Cannot Have Moving Average Parameters

Is there a way around this? Thanks in advance.

The GJR GARCH model is probably most easily done using the GARCH instruction, and the use of moving average terms for that is covered in the User's Guide in section 9.3.4 (RATS v8) or 12.1.4 (RATS v7). To add those to a FRML definition, you would need to use the lag of whatever series (probably called "u") that you're using for the models residuals.
TomDoan

Posts: 2720
Joined: Wed Nov 01, 2006 5:36 pm

### Re: GARCH with an ARMA mean equation

Thanks TomDoan, however I am not sure I understand how to add the lags of u in the frml.

The problem I have is that I need to estimate the model through the maximize command because my garch specification is non-standard (it includes two time dummies multiplied with u^2_t-1 and h_t-1). Let me show you what I have

Code: Select all
`open data C:\Program Files\Estima\WinRATS 7.2\at.txtdata(format=free,org=columns) 1 287 atlinreg at# constant at{1} frml(lastreg,vector=beta) meanfnonlin(parmset=meanparms) beta*set uu = %seesqset h  = %seesqset u  = 0.0*nonlin(parmset=garchparms) c a b d e fcompute c=%seesq,a=.29,b=.52,d=0.30,e=-0.74,f=0.00001set dummy = t>=232frml varf = c+a*uu{1}+b*h{1}+d*uu{1}*dummy{1}+e*h{1}*dummy{1}+f*dummyfrml logl = (u=at-meanf),(uu(t)=u**2),(h(t)=varf(t)),%logdensity(h,u)maximize(parmset=meanparms+garchparms,METHOD=BHHH,PMETHOD=BHHH) logl 6 *`

As you can see the garch specification has two dummies (multiplied with uu and h) that capture any differential effect after a specific date. My question is how to change the mean equation to accommodate an ARMA structure.

Thanks for the help and the patience
Nai_re_PAOK

Posts: 3
Joined: Thu Mar 31, 2011 10:24 am

### Re: GARCH with an ARMA mean equation

You need to do the following to define the FRML for the mean equation:

Code: Select all
`boxjenk(ar=1,ma=1,const,define=arma11) at / umodify arma11vreplace %mvgavge with ufrml(equation=arma11,vector=beta) meanfnonlin(parmset=meanparms) beta`

It's the combination of MODIFY and VREPLACE which substitute out series U for the %MVGAVGE.
TomDoan

Posts: 2720
Joined: Wed Nov 01, 2006 5:36 pm

### Re: GARCH with an ARMA mean equation

I see. This does it, great! Most obliged TomDoan, thanks.
Nai_re_PAOK

Posts: 3
Joined: Thu Mar 31, 2011 10:24 am