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 in determining the estimation power. The larger GARCH and ARCH effects are contained in the series, the better estimation power we get. Moreover, we conclude that for a given sum of GARCH and ARCH values being constant, the combination that has equal weight has the best estimation power. Finally and most importantly, based on the result from the fourth simulation test, we understand that as long as we get an estimated model in which both estimated GARCH and ARCH parameters are significant, we have at least ninety percent of the standardized residuals that are normally distributed with the properties of zero mean and unit variance