Simple Question on GARCH..!!!

tiko · May 21st, 2004, 6:14 am

Hi to all,I am modelling volatility of an interest rate, however, the distribution does have extremely high excess kurtosis, therefore GARCH does not converge to its long term mean, so i tried to remove outliers and the returns that are above the 3 sigmas level......i had to remove up to 25 observations from 400 observations for GARCH(1,1) to converge.......is this acceptable????

MikeM · May 21st, 2004, 6:36 pm

No. ...Well very rarely. The fact that you're asking the question suggests that you know something is wrong. Removing data is a slippery slope. Unless there is some fundamental reason for the outlier (some event occured that day that will never ever happen again in a million years), then you should leave the "outliers" in.3+ sigma events occur much more often than most simple models would suggest. The fact that your model doesn't account for these events suggest that there is something wrong with your model, not your data. In practice, these kinds of outliers rarely prevent you from creating a model that will explain most of the data. I would be surprised if you really had to resort to leaving out data to get the parameters for your model.

tiko · May 22nd, 2004, 7:11 am

Hi thx Mike for you help,i would really appreciate it if you could suggest a remedy, shall i use lags in my GARCH model???

MikeM · May 24th, 2004, 6:29 pm

Not promising anything, but can you give us more details? Can you tell us what the series is? Which GARCH specification are you using, GARCH(1,1), EGARCH? What do you mean when you say the model doesn't coverge to the mean? Does it never settle down to the mean, does it move to the mean too slowly on average, or does it actually diverge?As for the lags, I'm not sure if this is what you mean, but people are often tempted to use overlapping data to smoothe out bumps in their data. You can do this, but it's best avoided if you don't have to. Using overlapping returns produces lots of subtle distortions, and can easily lead you astray.

r2338 · May 25th, 2004, 6:08 pm

Hello, I'm not sure if this will help but here goes. When you say that your model won't converge to its long run mean, do you mean the volatility won't converge to its long run mean? If so, you may have a unit root in the variance of the series you're working on. You should test for this and if you find a unit root in the variance of your model, estimate an IGARCH model. I think the details are in Campbell, Lo and Mackinley. Otherwise, just try IGARCH in google and you'll get a ton of stuff coming back.R

tiko · May 26th, 2004, 4:36 am

Thx for all the help,The series that i am modelling is on t-bills interest rates of an emerging market and actually the series looks very funny, and i am using GARCH(1,1) and what i meant by the series does not converge it does actually diverge for its long term mean, what do u mean by overlapping data to smoothe out bumps in their data..??? Can somebody give me some pointers with IGARCH or EGARCH, i am sorry to ask such a basic question...!!!!I have attached the series in excel if somebody is interested to take a look...

Oinker · May 26th, 2004, 11:37 am

...exponentially weighting the time series will have a smooothing effect...

MikeM · May 26th, 2004, 4:09 pm

I wasn't suggesting that you smoothe the data ...actually I was trying to discourage that approach.

N · May 26th, 2004, 9:22 pm

Hi to all,I am modelling volatility of an interest rate, however, the distribution does have extremely high excess kurtosis, therefore GARCH does not converge to its long term mean, so i tried to remove outliers and the returns that are above the 3 sigmas level......i had to remove up to 25 observations from 400 observations for GARCH(1,1) to converge.......is this acceptable???? For technical reasons, there are actually two solutions to your GARCH model for IR. I suggest that you never remove observations. You may want to try a easier problem like the volatility in the S&P 500 index where there is only one solution.Newton

tiko · May 27th, 2004, 6:05 am

Hi there, thx to all for replying...If you could elaborate Newton on your idea..!!!In the meatime, i 've tried to use as well moving averages and EWMA to model volatility as well....would you think that EWMA and moving averages could do a better job at this job than IGARCH???