Asymmetry, Fat-tail and Autoregressive Conditional Density in Daily Stocks Return Data

Abstract

This paper focuses on the study of unbiasedness and efficiency of the maximum likelihood estimates of the GARCH (1,1) model volatility parameters when the error distribution assumed is Johnson s SU under varying skewness and kurtosis levels. The study is based on a simulation experiment and a real application to daily returns of five stock indices. In general the ML estimates of volatility parameters are found to be unbiased with high efficiency when the true distribution is asymmetric and fat-tailed for all levels of skewness and kurtosis and all parameter levels. Models with time-varying shape parameters are found to give a better fit than models with constant shape parameters.