Replies to This Discussion

Permalink Reply by Michael Gutmann on May 27, 2009 at 2:53pm

Sam,
I had the same question. I began with a crude estimate of (omega, alpha, beta) = (0.02, 0.90, 0.08) -- they sum to 1. From this I was able to generage a GARCH model of S&P500 historical volatility that closely matched the VIX. I thought that quite impressive, since the GARCH model used just the S&P500 daily close and the VIX is based entirely on option chain bid-ask prices. I shared a spreadsheet with you of this, below. But again, I would like to figure out, in general, the technique for determining the omega, alpha, beta values. If you find out anything, please let me know. Thanks, Mike G.

Attachments:

• SP500 Tests x1.xls, 386 KB

• ▶ Reply

Permalink Reply by Haim Shalit on May 31, 2009 at 3:53am

Mike
Very impressing analysis. But you need to be sure that you have a martingale series of errors terms, i.e., that you have cleaned up all seasonality factors from the series before you Garch it. I will try your series in eviews to see if the GARCH parameters are reasonable.
Cheers
Haim

• ▶ Reply

Permalink Reply by Michael Gutmann on September 6, 2009 at 11:51am

Haim Shalit,

Thank you for the reply here. I reviewed the math of martingale series at Wikipedia but do not know how to apply the theory to the price data as you suggest. Would it be possible for you to briefly describe what is to be done and provide a reference so that I can learn the technique you alluded to?

Many thanks,
Mike

• ▶ Reply

Permalink Reply by Tom on June 3, 2009 at 10:16pm

Thank you very much for you time and your advice. It worked as charme. I got the values and they are very close to the values extracted from EVIEWS. Thank once again.....

Sam

• ▶ Reply

Permalink Reply by Michael Gutmann on September 6, 2009 at 11:52am

Sam,

I have not used EVIEWS. Is it correct that the EVIEWS software generated (somehow) values of omega, alpha and beta that are close to the choices I landed on as a first approximation?

Thanks for your feedback,
Mike Gutmann

• ▶ Reply

Permalink Reply by yasin mahmood on November 8, 2010 at 7:49pm

Hi Michael,
I am new member and i want to know how i can implement GARCH in my thesis, caan you please tell me the procedure of it? i am working to study the volatality of KSE pakistan, so please guide me how i will prepare data and measure coefficients etc.

Regards,

Yasin Mahmood

• ▶ Reply

Permalink Reply by Arun Kumar Saha on May 28, 2009 at 10:35am

I think you should try with Logarithmic return not absolute return

• ▶ Reply

Permalink Reply by Joseph Foutz on May 28, 2009 at 4:24pm

There is a very large body of literature on estimating GARCH. Generally you can use the two-step estimator as an approximation, or just do the first step to yield starting values for your iterative optimization. Looking through my bookshelf, I found a brief description in Greene’s Econometric Analysis using OLS and a more thorough treatment in Tsay’s Analysis of Financial Time Series using ML.

• ▶ Reply

Permalink Reply by Michael Gutmann on September 6, 2009 at 11:54am

Joseph Foutz,

What textbook do you recommend as both introduction to GARCH as well as enough material to make use of GARCH; i.e., understand the theory behind the generation of omega, beta and alpha? Or is it as simple as the econometricians running OLS passes to fit the data? Sorry, I'm quite new to econometrics.

Thanks,
Mike Gutmann

• ▶ Reply

Permalink Reply by Joseph Foutz on September 8, 2009 at 8:53pm

I’ve cited Greene and Tsay already. Arup (below) cites Hamilton, which I used in a time series class. It’s a pain to read. And odd – example, where anyone else on earth would say “matrix form” he says “state space form” – which by some miracle doesn’t actually boggle the mind when he starts talking about state space models… Hamilton does not even BEGIN to address actually computing anything he talks about, but he represents the state of how things are taught. I think Tsay is your best bet on GARCH. Greene is also good. All three should be available at reasonably well equipped academic libraries. Gujarati doesn’t really cover GARCH, but he’s my all time favorite econometrics text author.

Also, manuals to commercial statistics programs can be your friend even if you don’t use that system. They cite basically everything you need to know about the theory of the model and how to estimate it. My favorite, of course, comes from my favorite statistics package – Stata – but sadly StataCorp doesn’t put the manuals online. The JMulTi docs are frequently good. Thinking of JMulTi, you might find it to be a nice (and free) alternative to doing some of this stuff in Excel, or verifying that your Excel calcs are in the ballpark.

• ▶ Reply

Permalink Reply by Michael Gutmann on September 20, 2009 at 11:39am

Joseph,
Many thanks for the detailed recommendations. I'm following up with the Tsay text and JMulTi.
--Mike

• ▶ Reply

Permalink Reply by arup guha on September 8, 2009 at 3:15am

hamilton. its a monster though, must warn you :)
Christian Gourieroux: arch models and financial applications is another good book

• ▶ Reply

• ‹ Previous
• 1
• 2
• Next ›
• Page