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In contrast to the traditional time series analysis, which focuses on the modeling based on the first two moments, the nonlinear GARCH models specifically take the effect of the higher moments into modeling consideration. This helps to explain and model volatility especially in financial time series. The GARCH models are able to capture financial characteristics such as volatility clustering, heavy tails and asymmetry. In much of the literature available for the GARCH models, the methods of estimating parameters include the MLE,GMM and LSE which have distributional and optimality limitations. In this book, the Optimal Estimating Function(EF) based techniques are derived for the GARCH models. The EF incorporate the Skewness and the Kurtosis moments which are common in financial data. It is shown using simulations that the Estimating Function (EF) method competes reasonably well with the MLE method especially for the non-normal data and hence provides an alternative estimation technique.Financial analysts, Econometricians and Time series scholars will find this book important in teaching and in risk computation.