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Looking at volatility of stock returns, what is the best model to use? I know there are as many answers as stocks, but has anyone studied if there are some similarities?I am working on a project, where I am interested in doing forecasting. I am looking at different models, mostly GARCH in its various forms. Any suggestions on other models that could actually be good? I would like to come up with a result, like to say that for these kind of stocks (e.g. a specific business sector) this model with parameter values around this is good, and for these stocks....The time for the project is rather short, so I am not trying to learn all kinds of exotic stochastic volatility models, which has to be fitted with MCMC or some other time consuming techniques. After all I want to test the models for hundreds of different stocks, and there is no use if it take me 15 minutes to fit the parameters for each stock. //muzzex

Hi MuzzexThere is no BEST model.You should study the particular characteristics of the stock.For example,you could use a EGARCH if the is a strong skew in the returns. Sometime the less complicated models work better. The improvement made by more sofisticated models is too little, but it demands a huge effort.

I am a strong believer in models that minimize the use of historic data, and instead rely on what the market implies about the future at a given moment in time. So any ARCH model or exponentially-weighted model will be at least third on my list.For this, stochastic vol models, like the Heston model, are usually my preffered method. Granted, this is probably more than you need or have time for on a short project.A close second choice is any calibrated local vol model. If you are only looking at near term volatility forecasts (so called "forward rates" of vol), then the Dupire formula is very fast and easy to use and implement. Several fitting algorithms will give you more accurate expectations beyond that horizon if you have time to program them...Hope this helps...

I am also starting to think that the GARCH models are not that good.I have tried to see whether the time window one uses for estimating the parameters have a influence on the values.Using a time interval of 500 return data, I get values between 0.01 and 0.8 for both regression parameters (innovations and lagged volas). Seems like it is a pure bingo what parameter one get. For the forecasting it makes a big difference.Also, I have seen that the models using EGARCH or some other modified GARCH such as PGARCH or TGARCH show better AIC or BIC (information criterias used for model selection) values. Especially using t or general error distribution give better goodness-of-fit results.But when I do forecasting with these models, and look at mean absolute error or root mean squared error MAE, RMSE (I am using a out-sample region here, with new data, not used for the parameter fitting) , they do not give the same results. To do forecasting it seems better to use the classical GARCH models, however still with t or GED distributed innovations.I have only been looking at two stocks so far, but still I think this is rather strange. Anyone has some experience with this, or is it only my codes that needs to be rewritten?Thanks for the answers..

Well I did the same kind of study on an index volatility for my DEA's final report and reached the same conclusion... I tried Egarch and all other X-garch model under a T and GED distribution...even if bic, aic and other Kolmogorov tests are better than for a GARCH model, I concluded that the information which was brought by those more complicated models was not so important in comparison with the information included in a garch model and it was easier too use a garch model to do forecast.That means that simplicity is sometime better.B

Hi b00008361,would be interesting to have a look at your DEA report?Thks

I agree with derivababy,what is DEA by the way?

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I am still looking at the forecasting properties.I use Splus to fit the model parameters to data. To see what kind of models perform the best, I do some testing on the forecasted data.I use an out-sample, and forecast with data, and compare with the given data in the out-sample.When I want to compare the models, I just use the squared returns as realized vola (well, square root). I think Splus (and MatLab) calculate the observed vola somewhat different.The thing is that when I compare the goodness-of-fit with simple models, such as moving average (mean of past say 4 or 10 observations), these other models sometimes perform better.I thought the GARCH models should be better in this case, or it is because Splus and MatLab use another observed vola, and I calculate my moving average forecasts with squared returns.Can someone help me on this? I think it is a bit strange, but what other amout than squared returns, can be used as to describe daily observed volatility? (Just to calculate a mean term, hardly makes any big difference when looking at log returns, because it is small)Thanks, Muzzex