Chapter 2 - A review of asymmetric conditional density functions in autoregressive conditional heteroscedasticity models

Abstract

This chapter provides a review of the use of asymmetric density functions in models of Autoregressive Conditional Heteroscedasticity (ARCH). The coverage of the models in this chapter is restricted to only considering discrete time Generalized Autoregressive Conditional Heteroscedasticity (GARCH) processes with asymmetric conditional distributions captured by known parametric forms. It is also found that skewness varies with size and across the business cycle, with relatively larger negative skewness found in times of favorable economic conditions and smaller negative skewness evident in less favorable times. While two different parameterizations of a density should produce the same outcome, there may be practical differences, such as sensitivity to initial values or speed of estimation. The double-gamma distribution has the advantage that it provides a convenient decomposition of the distribution into positive and negative components. Only the capital gains element of the index is used, no attempt is made to allow for the inclusion of dividends in the returns calculation or the calculation of the excess return over a risk-free rate of interest.