This article investigates the presence of long term memory of returns in south African and Kenyan financial markets over a period 1995-2010. Empirical results indicate significant presence of linear autocorrelation of order three for NSE20 index and autocorrelation of order one for TOP40 index. There is strong evidence of changing variance for both indices in addition to more autocorrelation between absolute returns for both markets. Theoretical autocorrelation function is fitted and parameters estimated. Different ARCH type models are conditioned on normal distribution and A-PGARCH model based on absolute daily returns seems to significantly outperform four other models (TGARCH, GARCH, GARCH-M and GJR-GARCH) in modeling the changing variance and volatility asymmetry in the two emerging markets.
Keywords: GARCH models, Long Memory, Volatility asymmetry, Leptokurtic returns