Van Niekerk, F.D.2022-01-122022-01-1219/8/20211999*http://hdl.handle.net/2263/83220Dissertation MSc)--University of Pretoria, 1999.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.en© 2021 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.UCTDHeteroscedastic volatilitySouth African financial marketsDissertation