Can one or or all comment on the validity of my approach?(1) Used 500 days of calibration data for parameter estimation of a GARCH(1,1) process and used best fit parameters to estimate future vol over a subsequent data set of 2500 days. (2) Calculated the rolling n-day vol (equally weighted) using n equal to a variety of observation lengths from one month (n=21) to five years (n=1260).(3) I then regressed the GARCH(1,1) estimate as well as the n-day vol estimates in (2) (X variable) on the future n-day vol (same intervals as in (2)) (Y variable) lagged such that the X and Y estimates relied on adjacent but completely independent data (ie, X as GARCH(1,1) used data 1-500 for calibration and first data point in series, Y as 60-day vol used data 501-560 for first data point in Y-series).(4) I asserted that because the GARCH(1,1) estimate using 500 days of calibration data had higher regression coeffs and t-stats than any of the regressions run using n-day vol for any n (for argument's sake, assume this was universally the case, though GARCH did in fact have lower coefficients for regressions on some future n-day vol lengths), that GARCH(1,1) had superior predictive power than simple rolling volatility.Boss counter-asserted that my statement was flawed since the GARCH estimate relied on 500 days of data while certain of the rolling vol estimates as predictors relied on less data. Thus, in order to assess GARCH's benefit any GARCH estimate regression would need to be compared ONLY to its corresponding rolling vol regression (ie, 40-day rolling vol as predictor versus GARCH(1,1) using 40 days for calibration data). Certainly, I can see how he could say that, but it seems to me that 'apples-to-apples' in this case isn't feasible since the GARCH estimate is fundamentally different than a simple standard deviation calculation. Thus, my assessment is valid since we'd never try to fit a GARCH model using only 20 days of data and GARCH using 500 days did better than any of the rolling vol estimates.

Last edited by CTD on November 3rd, 2008, 11:00 pm, edited 1 time in total.

A GARCH(1,1) is very similar to an exponentially weighted rolling vol, where the weighting is optimallydetermined by the MLE. So, I think the right comparison is against the best rolling n-day vol., where nis optimally determined.When all is said and done, I expect all these predictors will be inferior to ones also using forward-looking marketdata: option implied vols, VIX futures, etc.regards,

Last edited by Alan on November 3rd, 2008, 11:00 pm, edited 1 time in total.

Agreed regarding your interpretation of GARCH and interesting thought with implied vol--have you done anything similar to this? Certainly one could mimic VIX for different markets using options data...running something similar to the above, GARCH(1,1) still seems to perform approximately 20% better than straight VIX as a predictor for SP500 market vol

Yes, I did exactly that many years ago, when I worked for a money manager specializing in equity derivatives.The best predictors back then were GARCH/implied vol. mixtures, adjusted for some seasonalities.(Straight VIX is well-known to be biased high)If I was doing it again today, I would consider those previous models way too naive.

That's interesting. Using GARCH in place of simple rolling vol rendered a rather significant improvement on performance as is (as we'd expect). It'll be interesting to see how much better still I'm able to do. Though given this isn't completely central to my process, I'd expect to hit a point of diminishing returns relatively quickly. Thanks for the input

GZIP: On