additional nonlinear terms in EGARCH model

[Gin]

Hi all,

I would like to estimate the following model within EGARCH framework.

change in prices = constant + a1*X1*(1 + g1*Dummy1+ g2*Dummy2) + a2*X2*(1 + g1*Dummy1+ g2*Dummy2) + a3*X3*(1 + g1*Dummy1+ g2*Dummy2)

log(variance) = constant + USUAL VOLATILITY TERMS + b1*X1*(1 + gamma1*Dummy1+ gamma2*Dummy2) + b2*X2*(1 + gamma1*Dummy1+ gamma2*Dummy2) + b3*X3*(1 + gamma1*Dummy1+ gamma2*Dummy2)

where a1, a2, a3, b1, b2 ,b3 , g1 and g2 are coefficients to be estimated. a1 to b3 varies for regressors and g1, g2 , gamma1 and gamma2 are the same for subperiods, Dummy1 and 2 indicate dates.

Is it possible/makes sense to estimate such model with additional nonlinear terms? How can I add the nonlinear terms in the conditional variance equation?

Looking forward for discussion.

Thanks & best

[Gin]

Hi all,

I have tried to code the above model and estimate it using ml.

Code: Select all

''' declare starting value from existing nln-linear estimation equation nls_eq.ls y= c+ a1*X1*(1 + g1*Dummy1+ g2*Dummy2) + a2*X2*(1 + g1*Dummy1+ g2*Dummy2) + a3*X3*(1 + g1*Dummy1+ g2*Dummy2) coef(1) const = nls_eq.@coefs(1) coef(2) gam gam(1) = nls_eq.@coefs(3) gam(2) = nls_eq.@coefs(4) coef(15) be be(2) = nls_eq.@coefs(5) be(3) = nls_eq.@coefs(6) ''' get starting value from an existing egarch(2,1) model equation start.arch(2, 1, asy=1, egarch) y= c+ a1*X1*(1 + g1*Dummy1+ g2*Dummy2) + a2*X2*(1 + g1*Dummy1+ g2*Dummy2) + a3*X3*(1 + g1*Dummy1+ g2*Dummy2) coef(1) a1 = start.@coefs(7) ' the deterministic term coef(2) alpha alpha(1) = start.@coefs(8) alpha(2) = start.@coefs(9) coef(1) lambda = start.@coefs(10) ' coefficient for the leverage effect coef(1) bet = start.@coefs(11) ''' starting value for coeffecients in the variance equation are simply set to existing value of coeffs from the initial nls_eq coef(15) b b(1) = be(1) b(2) = be(2) b(3) = be(3) b(4) = be(4) b(5) = be(5) b(6) = be(6) b(7) = be(7) coef(2) g gamma(1) = gam(1) gamma(2) = gam(2) ' set presample values of expressions in logl smpl @first+1 @first+1 series sig2 = nls_eq.@se ' starting value for the variance is set to regression standard error of nls_eq ''' set up EGARCH likelihood logl egarch egarch.append @logl logl egarch.append res = y - a0 - be(1)*X1*(1- gam(1)*Dummy1 - gam(2)*Dummy2) - be(2)*X2*(1- gam(1)*Dummy1 - gam(2)*Dummy2) - be(3)*X3*(1- gam(1)*Dummy1 - gam(2)*Dummy2) egarch.append log(sig2) = a1 + alpha(1)*ABS(res(-1)/@SQRT(sig2(-1))) + alpha(2)*ABS(res(-2)/@SQRT(sig2(-2))) + lambda*res(-1)/@SQRT(sig2(-1)) + bet*LOG(sig2(-1)) + b(1)*X1*(1+ gamma(1)*Dummy1 + gamma(2)*Dummy2) + b(2)*X2*(1+ gamma(1)*Dummy1+ gamma(2)*Dummy2) + b(3)*X3*(1+ gamma(1)*Dummy1 + gamma(2)*Dummy2) egarch.append logl = log(@dnorm(res/@sqrt(sig2))) - log(sig2)/2 ''' estimate and display results smpl @first+1 @last egarch.ml(showopts, m=800, c=0.0001) show egarch.output smpl @all

However, eviews tells me that
" Illegal lag or index specification for coefficient A0 in "RES =
Y - A0 - BE(1)*X1*(1- GAM(1)*Dummy - GAM(2)*" in "DO_ EGARCH.ML
(SHOWOPTS, M=800, C=0.0001)".

As this part of estimation is really important to me... I would appreciate any suggestion.

Thanks!

[EViews Gareth]

Have you defined a0 anywhere?

If it is defined as a coef, you probably need a0(1)

[Gin]

Hi Gareth,

thanks for replying. I also just have figured it out..

However, now I have another problem when running the above code.
eview tells me
"Missing values in @LOGL series at current coefficients at
observation 12/17/2008 in "DO_ EGARCH.ML(SHOWOPTS,
M=800, C=0.0001)".
"
Have I missed sth in the part of presample value setting?

Code: Select all

' set presample values of expressions in logl smpl @first+1 @first+1 ' very first obs is NA series sig2 = nls_eq.@se ' starting value for the variance is set to regression standard error of nls_eq

I've checked the coefficients they are all properly set... Can you give me a hint of what could be wrong?

Another quick question, is it possible to directly specifiy nonlinear terms within " equation egarch.arch ... " in the mean and variance equation?

Thanks & best

[EViews Glenn]

In the mean, yes. In the variance, no.