Asymmetry, Fat-tail, and Autoregressive Conditional Density in Financial Return Data with Systems of Frequency Curves

Asymmetry and fat-tail are both stylized facts of financial return data. Many asymmetric and fat-tailed distributions have been used to model the innovation in autoregressive conditional heteroskedasticity (ARCH) models. This article introduces two more distributions from systems of frequency curves into the ARCH context: Pearson’s Type IV and Johnson’s SU. Both distributions have two shape parameters and allow a wide range of skewness and kurtosis. We then impose dynamics on both shape parameters to obtain autoregressive conditional density (ARCD) models, allowing time-varying skewness and kurtosis. The quasi-maximum likelihood estimates (QMLE) of volatility parameters obtained from these distributions are found to have high efficiency in a simulation study when the true distribution is asymmetric and fat-tailed. ARCD models with these distributions are applied to the daily Standard & Poor 500 index return data. Models with time-varying shape parameters are found to give better fit than models with constant shape parameters.