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GARCH forecast for EGARCH model
Posted: Tue Mar 12, 2013 12:28 am
by kiber_master
Hello!
Could you clarify the formula for GARCH forecast for EGARCH model, when assymetry order = 0? I think, there is some features or even errors in such cases. I've got too small figures in comparison with GARCH on sample period or with the case assymetry = 1.
I use last patch of E7.
Thank you.
Re: GARCH forecast for EGARCH model
Posted: Tue Mar 12, 2013 7:47 am
by EViews Gareth
I believe the forecast just uses the formula given in the representations view.
Re: GARCH forecast for EGARCH model
Posted: Wed Mar 13, 2013 7:27 am
by kiber_master
There is no exact formula for GARCH forecast in documentation. I've substituted resids with @SQRT(GARCH) on the forecast period (I suppose, it's correct), and the result differs from EViews output. Although, using this approach I get the same results with EViews output when Assymetry is positive.
Please, check your formula in the program. Is it surely correct?
Re: GARCH forecast for EGARCH model
Posted: Wed Mar 13, 2013 8:53 am
by EViews Gareth
As I said, the formula used in the representations view is what is used for the forecast. The only question is what happens with pre-sample values. Here's a program that replicates them:
Code: Select all
create u 1000
rndseed 1
series y=nrnd
series x=nrnd
equation eq1.arch(asy=0, egarch, z) y c x
eq1.fit yf yse ygarch
'first observation
smpl @first @first
!pi = 4*@atan(1)
!p1 = exp(c(3))
!p2 = !p1*exp(c(4)*@sqrt(2/!pi))
!p3 = !p2*(eq1.@ssr/eq1.@regobs)^c(5)
series mygarch = !p3
'other obs.
smpl @first+1 @last
mygarch = exp(C(3) + C(4)*ABS(RESID(-1)/@SQRT(mygarch (-1))) + C(5)*LOG(mygarch (-1)))
Re: GARCH forecast for EGARCH model
Posted: Wed Mar 13, 2013 11:32 pm
by kiber_master
I did what you offered: mygarch and ygarch are not equal...
Re: GARCH forecast for EGARCH model
Posted: Thu Mar 14, 2013 12:02 am
by EViews Gareth
And you're sure you're using the latest version of EViews? I've run that program on three different PCs and got the same results on each.
Re: GARCH forecast for EGARCH model
Posted: Thu Mar 14, 2013 1:01 am
by trubador
I get the same results too...
Re: GARCH forecast for EGARCH model
Posted: Thu Mar 14, 2013 9:38 pm
by kiber_master
But what if I want to forecast GARCH starting with 1001? I have no resids for 1001, so instead of ABS(RESID(-1)/@SQRT(mygarch (-1))) I should use @SQRT(2/4*@atan(1))), am I right?
Re: GARCH forecast for EGARCH model
Posted: Fri Mar 15, 2013 8:10 am
by EViews Gareth
You can calculate the resid out of sample from the mean equation:
Code: Select all
create u 1100
rndseed 1
series y=nrnd
series x=nrnd
smpl 1 1000
equation eq1.arch(asy=0, egarch, z) y c x
smpl @all
eq1.fit yf yse ygarch
series myresid = y-c(1)-c(2)*x
'first observation
smpl @first @first
!pi = 4*@atan(1)
!p1 = exp(c(3))
!p2 = !p1*exp(c(4)*@sqrt(2/!pi))
!p3 = !p2*(eq1.@ssr/eq1.@regobs)^c(5)
series mygarch = !p3
smpl 2 1100
mygarch = exp(C(3) + C(4)*ABS(myRESID(-1)/@SQRT(mygarch (-1))) + C(5)*LOG(mygarch (-1)))
Re: GARCH forecast for EGARCH model
Posted: Sun Mar 17, 2013 11:04 pm
by kiber_master
But what if I want to forecast GARCH starting with 1001? I have no resids for 1001
Your code is not for this case.
Re: GARCH forecast for EGARCH model
Posted: Mon Mar 18, 2013 11:16 am
by EViews Gareth
ok, it works the same way:
Code: Select all
create u 1100
rndseed 1
series y=nrnd
series x=nrnd
smpl 1 1000
equation eq1.arch(asy=0, egarch, z) y c x
smpl 1001 @last
eq1.fit(f=na) yf yse ygarch
smpl @all
series myresid = y-c(1)-c(2)*x
'first observation
smpl @first @first
!pi = 4*@atan(1)
!p1 = exp(c(3))
!p2 = !p1*exp(c(4)*@sqrt(2/!pi))
!p3 = !p2*(eq1.@ssr/eq1.@regobs)^c(5)
series mygarch = !p3
smpl 2 1100
mygarch = exp(C(3) + C(4)*ABS(myRESID(-1)/@SQRT(mygarch (-1))) + C(5)*LOG(mygarch (-1)))