A Comparison of Several Maximum Likelihood Based Methods for Estimating GARCH Model Parameters, Volatility and Risk

It has become common practice to fit GARCH models to financial time series by means of pseudo maximum likelihood. In this study we investigate the behaviour of several maximum likelihood based methods for estimating the Garch model parameters and for estimating volatility and risk measures (VaR and expected shortfall). We consider NIG, skewed-t, t and nonparametric kernel densities for this purpose and compare the efficiency of the resulting estimates with those based on the normal distribution. The NIG based approach is found to be competitive with the other methods in most of the cases considered. [email protected]) ∗ JH Venter is Professor at the Centre for Business Mathematics and Informatics, Potchefstroom University for CHE, Potchefstroom 2520, South Africa. He can be contacted by phone (27-18-2992551) or by E-mail ( . PJ de Jongh is also Professor at the Centre for Business Mathematics and Informatics, Potchefstroom University for CHE, Potchefstroom 2520, South Africa. He can be contacted by phone (27-18-2992585) or by E-mail ([email protected] ).