GARCH forecast algorithm?

[ycy88]

Good day,

I'm using E-views 7

I would like to know the algorithm used by E-Views to forecast GARCH variance (static forecast).
I tried to reproduce the same results in Microsoft Excel but failed. I couldn't figure out the algorithm E-Views used for the forecast.

Also, I would like to know the algorithm used in Proc>Make GARCH Variance Series as well.

Thanks in advance!

[ycy88]

Anyone could help, please?

[trubador]

GARCH estimation and forecasting are not specific to any software. You can find all the details you need in any econometrics/time series textbooks...

[ycy88]

GARCH estimation and forecasting are not specific to any software. You can find all the details you need in any econometrics/time series textbooks...

I understand. But I had a hard time figuring out how E-Views managed to get the forecast for the first observation.

For example, I have data with 2000 observations. I used the first 1000 observation to construct a AR(1)-GARCH(1,1) model. Then, I made a forecast for the entire data set. Eviews generates estimates for variances from observation 3 to 1999. I could not figure out how Eviews managed to get the estimate for observation 3, let alone for the rest of the estimates. I do not know the term "b[cond. variance for t-1]" in h(t|t-1) = w + a[error for t-1]^2 + b[cond. variance for t-1] for observation 3.

[trubador]

Conditional variance is the GARCH term (h variable) itself that you are trying to estimate. cond. variance for t-1 is the lagged term of h(t|t-1). Your model estimates the w, a and b coefficients and generates the conditional variance based on these parameter results. For more details, please refer to textbooks...

[ycy88]

I understand. But I had a hard time figuring out how E-Views managed to get the forecast for the first observation.

For example, I have data with 2000 observations. I used the first 1000 observation to construct a AR(1)-GARCH(1,1) model. Then, I made a forecast for the entire data set. Eviews generates estimates for variances from observation 3 to 1999. I could not figure out how Eviews managed to get the estimate for observation 3, let alone for the rest of the estimates. I do not know the term "b[cond. variance for t-1]" in h(t|t-1) = w + a[error for t-1]^2 + b[cond. variance for t-1] for observation 3.

I think I understand the GARCH formula. However, I have trouble trying to estimate the first conditional variance. Referring to the example above, what value should I use for the term "b[cond. variance for t-1]" for the first observation (observation number 3 in the example above)? The previous conditional variance is not available due to the fact that it is the first observation.

[trubador]

I think you are asking for the initialization. EViews refers to this problem as backcasting of the presample variance. Common practice is to set the unconditional variance as the initial value. However, by default, EViews compute the residuals of the mean equation via using the coefficient values, and then computes an exponential smoothing estimator of the initial value. You can change the smoothing parameter values from 0.1 to 1.

[ycy88]

I think you are asking for the initialization. EViews refers to this problem as backcasting of the presample variance. Common practice is to set the unconditional variance as the initial value. However, by default, EViews compute the residuals of the mean equation via using the coefficient values, and then computes an exponential smoothing estimator of the initial value. You can change the smoothing parameter values from 0.1 to 1.

Thank you very much, trubador, for you have enlightened me in this matter! I'm not aware of the backcasting method to estimate the initial conditional variance :D