GARCH forecast for EGARCH model

[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.

[EViews Gareth]

I believe the forecast just uses the formula given in the representations view.

[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?

[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:

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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)))

[kiber_master]

I did what you offered: mygarch and ygarch are not equal...

[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.

[trubador]

I get the same results too...

[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?

[EViews Gareth]

You can calculate the resid out of sample from the mean equation:

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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)))

[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.

[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)))