Volatility estimation plays an important role in the fields of statistics and finance. Many different techniques address the problem of estimating volatilities of financial assets. Autoregressive conditional heteroscedasticity (ARCH) models and the related generalized ARCH models are popular models for volatilities. Multivariate approaches to GARCH models, such as Engle's Dynamic Conditional Correlation GARCH (DCC-GARCH), allow for estimation of multiple financial asset volatilities and covariances. However, the parameters of the DCC-GARCH model are typically estimated with Maximum Likelihood Estimation (MLE), which is greatly affected by outliers. Outliers in a DCC-GARCH model affect subsequent estimation of volatilities by the design of the model. These outliers may also affect volatility estimates of other financial assets within the same set of assets due to the correlated nature of the financial asset estimation.;This thesis reviews ARCH / GARCH modeling and robust estimation and proposes a robust estimation method for the DCC-GARCH model based on bounded deviance function estimation. This robust method of the DCC-GARCH model better estimates the volatilities of a set of financial assets in the presence of outliers. The thesis presents a study of the consistency of the robust method of the DCC-GARCH model along with simulation results to explore the characteristics of the robust method of the DCC-GARCH model estimation. For a better evaluation of the robust method, the thesis also examines the distribution structure of foreign exchange rate data. The thesis also discusses possible future topics and research in this field of study.
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