Financial time series with heteroscedastic volatility in the South African financial markets

Abstract

We investigate the issues surrounding linear time series models. Our specific interest is in stationary time series models and difference equations. We derive an analytical expression for the inverse of the matrix F characterising such difference equations using Vandermonde's matrix theory. We use these results to discuss the homoscedastic ARMA and heteroscedastic ARCH and GARCH type time series models. Finally we use the ARCH and GARCH type models to construct various asymmetric news impact curves for South African financial time series.