Stock price forecasting is a popular and important topic in financial and academic studies, and time series analysis is an advanced set of tools that is useful for this type of data. This study analyzes a time series of S&P 500 index returns data; and employs time series methods and ARMA modelling to predict S&P 500 index mean returns. Index return volatility is also analyzed and forecasted using GARCH modelling techniques. Multiple competing models are fitted and tested using Eviews software. Weekly observations of S&P 500 index returns from 2010 to 2016 are used to fit several conditional variance models, and the most preferred model is selected in order to forecast variance. The two most preferred conditional mean and conditional variance models are used to forecast values for the next ten weekly observations, and the forecasted values are compared with the actual data. The conditional variance results are of particular usefulness in risk modelling applications.