After Engle noticed high autocorrelation in squared returns, he suggested an ARCH model. Subsequently, Bollerslev suggested the GARCH model. The main advantage of the GARCH model is that it has much less parameters and performs better than the ARCH model.
The generalized autoregressive conditional heteroskedasticity (GARCH) model has only three parameters that allow for an infinite number of squared roots to influence the conditional variance. This characteristic enables GARCH to be more parsimonious than ARCH model. In brief, GARCH is a better fit for modeling time series data when the data exhibits heteroskedacisticity and volatility clustering. However, in some cases there are aspects of the model which can be improved so that it can better detect the features and dynamics of a particular time series. For example, a standard GARCH model fails in capturing the “leverage effects” which are observed in the financial time series. In other words, based on this model, good and bad news have the same effect on the volatility. To address this problem, several GARCH extensions were proposed. For a detailed discussion of extensions to the basic GARCH model that make GARCH modeling more flexible, you can refer to Zivot (2008).
Regards,
Dear Refk, thank you very much for your clear answer...
In an autoregressive AR(n) model, the current value of the process is a weighted sum of the past n values together with a random term. where the weightings are fixed and the random innovations are independent and identically distributed. This model is homoskedastic -- the random changes at each time step all come from the same distribution. (homo = same; skedastic = pertaining to scattering.)
Some real-world phenomena appear to be heteroskedastic instead i.e. they appear to have volatile periods followed by calm periods. The easiest way to do this is simply to specify what the particular distribution at a particular time will be. For instance, there is a lot more uncertainty in daytime electricity use than in nighttime electricity use, so if we were to model the electricity use at a particular time we might assume that the electricity use during the day would have a particular variance σDayσDay, and that the use during the night would have a lower variance σNightσNight. This is an ARCH model -- it's an AR model with conditional heteroskedacity (conditional on the current time).
On the other hand, perhaps the swings in volatility don't necessarily happen at particular times -- perhaps the times at which they occur are themselves stochastic. Instead of specifying exactly what the variance is going to be at each particular time, we might model the variance itself with an AR(p) model. This is a GARCH (generalized ARCH) model.
If you are referring to univariate conditional volatility models, such as ARCH(1) = GARCH(1,0) versus GARCH(1,1), the latter always fits financial data better than does the former.
Neither ARCH nor GARCH can capture asymmetry or leverage.
The only multivariate conditional volatility model that has mathematical regularity conditions, including invertibility, a valid likelihood function, and the asymptotic properties of consistency and asymptotic normality of the QMLE of the parameters is Diagonal BEKK.
In garch output, there are terms that I don't know them. What do garch0 and garch1 mean?
Both models are related to economic forecasting and measuring volatility.
ARCH is concerned about modeling the volatility of the variance of the series. Some of the real-time examples where ARCH model(s) applied: Stock prices, oil prices, bond prices, inflation rates, GDP, unemployment rates, etc.
GARCH is an extension of the ARCH model that incorporates a moving average component together with the autoregressive component. GARCH is the “ARMA equivalent” of ARCH, which only has an autoregressive component. GARCH models permit a wider range of behavior more persistent volatility.
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