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This study investigates the time series beaviour of daily stock returns of four firms listed in the Nigerian Stock Market from 2nd January, 2002 to 31st December, 2006, using three different models of heteroscedastic processes, namely: GARCH (1,1), EGARCH (1,1) and GJR-GARCH models respectively. The four firms whose share prices were used in this analysis are UBA, Unilever, Guiness and Mobil. All the return series exhibit leverage effect, leptokurtosis, volatility clustering and negative skewness, which are common to most economic financial time series. Except for Guiness, other series display significant level of second-order autocorrelation, satisfying covariance-stationary condition. These models were estimated assuming a Gaussian distribution using Brendt-Hall-Hall-Hausman (BHHH) algorithm's program in Eview software platform. The estimation results reveal that the GJR-GARCH (1, 1) gives better fit to the data and are found to be superior both in-sample and out-sample forecasts evaluation

On Modeling the Volatility of Nigerian Stock Returns Using GARCH Models