On Heteroscedastic, Skewed and Leptokurtic Log Returns and Spectral Density of Standardized Residuals

A search for a distribution which adequately describes the dynamics of log returns has been a subject of study for many years.Empirical evidence has resulted in stylized facts of returns.Arguably, in this study, the three components of returns, mean equation part, the changing variance part and the resulting residuals are determined and their corresponding parameters estimated within the proposed framework.Spectral density analysis is used to trace the seasonality component inherent in the standardized residuals.Empirical data sets from eight different indexes and common stock are applied to the model, and results tabulated in support of the resulting framework.