Question

Define in 200 words:  Garch (1,1) model

Answer 1

Answer-

Generalized Autoregressive Conditional Heteroskedasticity (GARCH) allows to support changes in the time dependent volatility, such as increasing and decreasing volatility in the same series.
GARCH, is an extended form of the ARCH model that incorporates a moving average component together with the autoregressive component.

GARCH(1,1) is used for a single time series. In GARCH(1,1) model, current volatility is influenced by past innovation to volatility. It is used for modeling of univariate finacial time-series, that simultaneously model both mean and variance equation.

Garch (1,1) model is used to derive conditional volatility estimates by using the standard Maximum Likelihood method using the numerical computation. The returns do not have a normal distribution, that they have long tails. It is reasonable to hypothesize that the long tails are due entirely due to garch effects, in which case using a normal distribution in the garch model would be appropriate, however using the likelihood of a longer tailed distribution turns out to give a better fit always most of the time.
GARCH (1,1) model explains volatility and its the most appropriate model for explaining volatility clustering and fat tails.
GARCH(1,1) model can be used to describe the stylized facts of volatility clustering and excess kurtosis however  asymmetric effects of positive and negative shocks on the conditional volatility are explained by this model.