One of the significant features of financial data that has won much attention is the volatility; because it is a numerical measure of the risk faced by individual investors and financial institutions. It is well known that the volatility of financial data often varies over time and tends to cluster in periods, i.e., high volatility is usually followed by high volatility, and low volatility by low volatility. The QML estimation procedure is illustrated with using daily return data for one stock in the Middle East Stock Exchange. The effects of outliers on modeling and forecasting the conditional variances in return series are also studied with this series.