Hello, guys:A rookie question: what is the advantage of garch over arch?I am going to have a interview with a stat-arb hedge fund and this question comes up to me while I am preparing.

QuoteOriginally posted by: atlantaquantHello, guys:A rookie question: what is the advantage of garch over arch?I am going to have a interview with a stat-arb hedge fund and this question comes up to me while I am preparing.If I remember correctly, a garch model is a parsimonious arch with infinite lags. And the garch parameter picks up a pattern where the a shock at e^2 decays over time.

Sometimes you need too many parameters to fit the data in an ARCH model... the GARCH model is a parsimonious alternative. By putting a sigma^2 (t-1) on your vol equation (Garch(1,1), for example), you usually end up with a model that wastes less info. The idea is pretty similar to the AR to ARMA improvement...

QuoteOriginally posted by: SNWKWSometimes you need too many parameters to fit the data in an ARCH model... the GARCH model is a parsimonious alternative. By putting a sigma^2 (t-1) on your vol equation (Garch(1,1), for example), you usually end up with a model that wastes less info. The idea is pretty similar to the AR to ARMA improvement...SNKW is probably more correct than me. The garch is a parsimonious version of a arch with lots of lags (and not infinite).A good question is why this is important and why we see large number of significant lags at arch models. My intutions says that is is because of volatility clustering. Since a lot of high vol observations tend to be in the sames places in time, the autoregressive patter of a Arch picks it up by showing statistically significant large number of lags. The garch fix it because now a shock will decay over time and when volatility cluster, the garch parameter picks up the same autoregressive pattern as a the large number of arch coefficients together.I think you should also brush up on the unconditional moments of the model (first, second and fourth). This will also brush up the restrictions on the parameters of them model (eg. why a+b<1).

Not 100% sure I got it right here, but I believe GARCH can accomodate exogenous variables in accounting for changes in volatility, whereas ARCH merely uses lagged values of previous volatility to predict future volatility.

QuoteOriginally posted by: CariocaBruceNot 100% sure I got it right here, but I believe GARCH can accomodate exogenous variables in accounting for changes in volatility, whereas ARCH merely uses lagged values of previous volatility to predict future volatility.Thats not right Bruce. Since you're dealing with maximum likelihood estimation, which is a flexible and general method, you can add pretty much add whatever you want in arch and garch models (and also in the mean equation). by the way, are you from rio de janeiro?