Dear Professor Alexander,

Let me start this email with my gratitude for writing the excellent series of books: “Market Risk Analysis”.

I have been studying the first two volumes and “Practical Financial Econometrics” is one of the most useful books on econometrics that I own.

I have been experimenting with the EGARCH(p,q) model and I wonder if there is a small errata in the formula for the long-term-variance at page 152.

Instead of computing the long-term-variance as you suggested by setting: sigma_t^2 = sigma_{t-1}^2, and use the fact that E(gz)) =0, I wrote the model as:

sigma_t^2 = exp(omega) * exp(g(z_{t-1}) * sigma_{t-1}^(2*beta)

If I now assume that sigma = sigma_t = sigma_{t-1} and take the expectation I find that:

Sigma^(2-2*beta) = exp(omega) * E[exp(g(z))]

or

log sigma^2 = ( omega + log(E[exp(g(z))]) ) / (1-beta)

If E[exp(g(z))] is zero then this matches formula (II.4.28), but this only happens if both gamma =1 and theta =0. In any other case the long term variance/volatility give in II.4.28 will give the wrong result.

Luckily you derive the value of E[exp(g(z))] just two pages later in equation (II.4.32), so I think the correct version is:

log sigma^2 = ( omega -gamma*sqrt(2/pi) + log(C ) ) / (1-beta)

Do you think the formula II.4.28 should be changed with the one above?

thanks

giancarlo pfeifer

## Possible errata for formula II.4.28 (EGARCH() long-term-var)

**Forum rules**

DISCLAIMER: We do not warrant or represent that this forum or its content is free of viruses, worms or other code that might be contaminating or destructive. We cannot guarantee that documents or files downloaded from the Site will be free from viruses and we do not accept any responsibility for any damage or loss caused by any virus. Accordingly, for your own protection, you must use virus-checking software when using the forum. You must not post or provide to us via the forum, any document or file which you believe may contain a virus. You must virus check any document or file which you intend to post or provide to us via the forum. You must ensure that any document or file you intend to post to the forum does not contravene any applicable laws or contravene any person's legal rights. We do not accept any responsibility for any damage or loss you may suffer.

### Who is online

Users browsing this forum: No registered users and 1 guest