Generalized
Autoregressive Conditional Heteroscedastic Time Series Models with Applications
This paper gives a survery of the univariate GARCH models for financial
time series with applications. ARMA models are reviewed at first. T hen, ARCH
and GARCH models are introduced with specifications, important properties,
estimation, and diagnostic evaluations. A more detailed analysis is implemented
to the GARCH (1,1) models with forecasting. Moreover, the properties of the
estimated parameters of the GARCH (1,1) models are explored by monte-carlo
simulations. ARMA-GARCH models, GARCH in Mean models and EGARCH models are also
covered briefly as an extension. As examples, Standard & Poor's 500 stock
price index and IBM stock price are used to fitting different models.