Forecast of variance by GARCH model

[Lyubov]

Good Day!

I'm using EViews 6.0.
I have such GARCH(1,1) model:

h(t|t-1) = w + a[error(t-1)]^2 + b[cond. variance(t-1)]

How EViews compute [error(t-1)]?

Is it forecast SE, which compute for main equation? And, if it's true, - how to compute forecast se?
(I find one formula in UserGuide: forecast se = s sqrt[1+x(t)'((X' X)^-1)x(t)]. But i can't understand what is X and x(t) in this formula)

[EViews Gareth]

http://forums.eviews.com/viewtopic.php?f=4&t=3900

[Lyubov]

http://forums.eviews.com/viewtopic.php?f=4&t=3900

Yes, I saw this topic. But it isn't what i want. I need to find out how to compute [error(t-1)].
And is EViews provide only forecast of variance for errors? And what about forecast of volatility?

[Lyubov]

http://forums.eviews.com/viewtopic.php?f=4&t=3900

Yes, I saw this topic. But it isn't what i want. I need to find out how to compute [error(t-1)].
And is EViews provide only forecast of variance for errors? And what about forecast of volatility?

I mean can i compute in EViews the forecast of volatility of dependent variable, for example, prices of stocks (from main equation) ?

[EViews Gareth]

I'm really not sure I understand your question.

[Lyubov]

I'm really not sure I understand your question.

I have such equations:


(1) - main equation, where y_t - dependent variable (price of stocks), x_t - independent variable (fond index)
(2) - equation for variance - GARCH(1,2).

I compute forecast of y_t (3) and variance of epsilon_t (4):


As i understand, terms "conditional variance" and "volatility" are the same. So, I have the forecast of volatility of errors on (4). Am I right?
Are the red dashed lines on graph (3) epsilon_t ?

And, can I forecast the volatility of y_t (not errors) in EViews ?

[trubador]

Again, the issue here is not related to EViews. Your equations are correct and the produced results look allright. EViews seems to be doing what it is supposed to be doing. You can obtain the conditional variance estimates via Proc/Make GARCH Variance Series. Also, you can generate (static/dynamic) forecasts of these values from the Forecast tab in the Equation dialog box. I believe you are having trouble with the concepts used in GARCH modeling, and therefore it would be a good idea to refer to a textbook before going any further in your analysis.

[Lyubov]

Again, the issue here is not related to EViews. Your equations are correct and the produced results look allright. EViews seems to be doing what it is supposed to be doing. You can obtain the conditional variance estimates via Proc/Make GARCH Variance Series. Also, you can generate (static/dynamic) forecasts of these values from the Forecast tab in the Equation dialog box. I believe you are having trouble with the concepts used in GARCH modeling, and therefore it would be a good idea to refer to a textbook before going any further in your analysis.

Thank you very much!
I have one more question. Maybe, it connected with topic http://forums.eviews.com/viewtopic.php?f=4&t=3900

If i have, for example, equation (2) and i want to compute variance for t=1. I must know variances for t-1 and t-2 (i.e. variance_0 and variance_-1)
I find formula for initial value:


So, i can compute variance_0 by this formula. And how can i compute variance_-1 ?

[trubador]

It will be same as variance_0. You will use this value for all the presample variances and squared residuals: variance_-1 = variance_-2 = ... = resid^2_0 = resid^2_-1 = resid^2_-2 =... = variance_0

[Lyubov]

It will be same as variance_0. You will use this value for all the presample variances and squared residuals: variance_-1 = variance_-2 = ... = resid^2_0 = resid^2_-1 = resid^2_-2 =... = variance_0

Thanks for you help, trubador.
And, i hope, the last question ))

I'm not sure, that i understand one thing correctly... :
epsilon_t, that used in equation for variance. Is it the forecast S.E., which we can save in Forecast Window ? Or something else?

[trubador]

It's the residuals. EViews stores the values into "resid" variable in your workfile after each estimation...

[Lyubov]

It's the residuals. EViews stores the values into "resid" variable in your workfile after each estimation...

Thanks yot very much! As i understand, RESID = real y - forecast y.
So, If we don't have real values for forecast's period, - we can't compute forecast of variance on this forecast's period ?

[Lyubov]

It's the residuals. EViews stores the values into "resid" variable in your workfile after each estimation...

Thanks yot very much! As i understand, RESID = real y - forecast y.
So, If we don't have real values for forecast's period, - we can't compute forecast of variance on this forecast's period ?

hmmm... RESID = real y - forecast y.
If, for example, i have model for period 2008 - 2009 years, and i want to make forecast on 2009-2010. I don't have real values of y on this period. (And EViews realy doesn't save residuals to the serial RESID).
But EViews do forecast of variance to period 2009-2010.

How EViews can do it, if epsilon_t = RESID, used in equation for variance, isn't know ?

[Lyubov]

And if i don't have real values of y to 2009-2010, i see N/A in series GARCH from 2009 to 2010 (i make it such way: Proc / Make GARCH variance series). But i have graph of forecast of variance from 2009 to 2010 (like (4)). What is it? How EViews can do this graph, if GARCH series is N/A to forecast period ?

[Lyubov]

I think, I understand the situation.

For dynamic foresast EViews uses values of forecast S.E. as epsilon in equation for variance. So, we can do forecast for many steps, even if we don't have real values of y for forecast's period.
For static forecast it uses series RESID (= real y - forecast y) as epsilon. And if we don't have real values for forecast's period, we can make static forecast only for one step.

Am I right?