Investigation of GARCH Models for the Estimation Power and Normality

The aims of the thesis are to investigate the estimation power and the normality of standardized residuals for Generalized autoregressive conditional heteroscedasticity models (GARCH). We facilitate the analysis by only dealing with GARCH(1, 1) models. We take use of MATLAB as the statistical programming tool for the simulation of the data and the estimation. We define the meaning of estimation power in three ways. Firstly, how close estimated expectation of estimators is to the actual value given a value of biasness. Secondly, another way to define the estimation power is by calculating Root Mean Square Error (RMSE) of estimated values. Finally, we define it by how large proportion of significant models we get. To analyze the estimation power, we perform three simulation tests to measure the biasness, the RMSE and the proportion of significant GARCH(1, 1) models. In addition, we analyze the normality by calculating the proportion of standardized residuals using the Jarque-Bera test. Based on the results from those three simulation studies focused on the estimation power, we conclude that when the number of observations increases, it reduces the biasness of the estimated parameters. Secondly, the size of the GARCH and ARCH parameters plays a major role i