Command for GJR and Bollerslev-Woolridge error in GARCH-Code

[morbo-23]

Hello,
i wrote my own logLikelihood-function for a GARCH-model.
I set up my own logLikelihood-function with help from the EViews sample programms. The errors are gaussian distributed.
How do I add the GJR-Coefficient (T-GARCH) in my Variance Equation?
ll1.append sig2 = omega(1)+alpha(1)*res(-1)^2 +beta(1)*sig2(-1)
I hope someone can help me.
Is there a command for Bollerslev-Wooldbridge robust errors in the logLikelihood-function?
Thanks!!!

[Zappa_F]

Hi morbo-23,

I wrote something that might help you. I am not sure, if it is really correct. But I'd appreciate it if you could take a look at it.
I have arbitrarily taken a AR(2) for the conditional mean.

Code: Select all

'################################################## 'AR(2) - GJR-GARCH(1,1) '################################################## 'turn to page of question in workfile pageselect test 'set counter which stops the time how long eviews needs to do the computation tic 'take first log naturalis difference of (in my case) real GDP series to get growth rate expressions series y = dlog(rgdp) ' declare coef vectors to use in conditional mean and GARCH equation coef(1) mu = .1 coef(2) phi = .1 coef(1) omega coef(1) alpha = .1 coef(1) beta = .8 coef(1) gamma = .2 ' get starting values for the parameters in GARCH equation which will be estimated by ML from ARMA(p,q) OLS estimation equation temp.ls y c ar(1) ar(2) mu(1) = temp.c(1) phi(1) = temp.c(2) phi(2) = temp.c(3) ' Define name of the logl object logl bedvar ' add a object named loglike to the logl object bedvar.append @logl loglike 'generate residuals of the ARMA(p,q) condittional mean bedvar.append res = y - mu(1) + @nan( - phi(1)*y(-1) - phi(2)*y(-2), 0) 'generate dummy for the GARCH equation bedvar.append dummy = @nan(@recode(res(-1)<0, 1, 0),0) 'define condtitional variance bedvar.append sig2 = @nan(omega(1) + alpha(1) * ( res(-1) )^2 + gamma(1)*( res(-1) )^2*dummy+ beta(1) * sig2(-1),1) ' Log-Likelihood function assuming Gaussian white noise errors. I was not exact regarding the first term which should say log(Pi) because for maximization the first derivative of loglike is taken and therefore the first (constant) terms drops out anyways bedvar.append loglike = @nan( - 0.5 * log( 2* 3.14 ) - 0.5 * log(sig2) - 0.5*( res )^2 , 1 ) 'do the algorithm default setting is the MARquardt algorithm bedvar.ml(showopts) 'skirmish ' Save information criteria scalar aic = bedvar.@aic scalar bic = bedvar.@schwarz scalar hqc = bedvar.@hq ' save the computation time in a scalar named elapsed scalar elapsed = @toc

Regarding your Bollerslev_Wooldridge error question: You said that you assumed a Gaussian error distribution if I understood you correctly. Then you do not need the quasi maximum likelihood approach. The parameter estimats do not change anyways. Only the variance-covariance matrix changes.

Do you know how to tell Eviews (in the code above) when maximizing the loglikelihood function to use the BHHH algorithm rather than Marquardt????

Sincerely yours,

Z

[trubador]

Do you know how to tell Eviews (in the code above) when maximizing the loglikelihood function to use the BHHH algorithm rather than Marquardt????

bedvar.ml(b,showopts)

[morbo-23]

Hi Zappa,

i solved the GJR-part in a similiar way.
I use a gaussian distribution for my errors. I used the one from the sample files. There is also a code for an ar(1)-garch model with t-distribution. Maybe the code can provide some help for writing an ar-garch-model.
Regarding the Bollerslev Robust Standard Errors: The Coeficients doesnt change, only the Covariance. But how do I calculate the robust Covariance? If you use the drop-down menu for ARCH-models you can simply choose bollerslev-robust-errors. In the programming manual you can find that h is the command for those robust errors. But it didnt work in my code.
I hope someone can help me with the calculation of the robust covariance (bollerslev-woolridge robust errors).
See my Code below:
f <- is a dummy-variabel that takes the value of 1 after a certain date
r_csi <- returns of the csi300 index
r_hs <- returns of Hang seng- Index
r_sp <- returns of S&P500
rl <- first lag of returns

Code: Select all

' set sample sample s1 2 2 sample s2 3 1590 smpl s2 ' get starting values from Gaussian ARCH equation eq1 eq1.ls r_csi c Di Mi Do Fr r_sp(-1) r_hs r_csi(-1) r_csi(-3) f*r_csi(-1) f*r_csi(-3) ' declare and initialize parameters coef(1) mu = eq1.c(1) coef(1) d1 = eq1.c(2) coef(1) d2 = eq1.c(3) coef(1) d3 = eq1.c(4) coef(1) d4 = eq1.c(5) coef(1) gs = eq1.c(6) coef(1) ls = eq1.c(7) coef(1) rl = eq1.c(8) coef(1) rl3 = eq1.c(9) coef(1) f_rl = eq1.c(10) coef(1) f_rl3 = eq1.c(11) coef(1) omega = 0.00004 coef(1) alpha = 0.15 coef(1) beta = 0.6 coef(1) gamma = 0.05 coef(1) dum = 0 ' set presample values of expressions in logl smpl s1 series sig2 = omega(1) series res = 0 ' set up GARCH likelihood logl ll1 ll1.append @logl logl ll1.append res = r_csi-mu(1)-d1(1)*Di-d2(1)*Mi-d3(1)*Do-d4(1)*Fr-gs(1)*r_sp(-1)-ls(1)*r_hs-rl(1)*r_csi(-1)-rl3(1)*r_csi(-3)-f_rl(1)*f*r_csi(-1)-f_rl3(1)*f*r_csi(-3) ll1.append sig2 = (omega(1)+alpha(1)*res(-1)^2 +beta(1)*sig2(-1)+gamma(1)*`res(-1)^2*(res(-1)<0))*(1+dum(1)*f) ll1.append z = res/@sqrt(sig2) ll1.append logl = log(@dnorm(z)) - log(sig2)/2 ' estimate and display output smpl s2 ll1.ml(showopts, m=1000, c=1e-5,b,h) show ll1.output

I hope someone can help me with the calculation of the robust covariance (bollerslev-woolridge robust errors).
Thanks