We investigated the presence of, and changes in, long memory features in the returns and volatility dynamics of S&P 500 and London Stock Exchange Using ARMA model. Recently, multifractal analysis has been evolved as an important way to explain the complexity of financial markets which can hardly be described by linear methods of efficient market theory. In financial markets, the weak form of the efficient market hypothesis implies that price returns are serially uncorrelated sequences. In other words, prices should follow a random walk behavior. The random walk hypothesis is evaluated against alternatives accommodating either unifractality or multifractality. Several studies find that the return volatility of stocks tends to exhibit long-range dependence, heavy tails, and clustering. Because stochastic processes with self-similarity possess long-range dependence and heavy tails, it has been suggested that self-similar processes be employed to capture these characteristics in return volatility modeling. The present study applies monthly and yearly Forecasting of Time Series Stock Returns in S&P 500 and London Stock Exchange Using ARMA model. The statistical analysis in s&p500 shows that the ARMA model for S&P500 outperforms to the London stock exchange and it is capable for predicting medium or long horizons using real known values. The statistical analysis in London Stock Exchange shows that the ARMA model for monthly stock returns outperforms to the yearly. The comparison between S&P 500 and London Stock Exchange shows that both market is efficient but S&P 500 have a high efficiency and London Stock Exchange have a semi strong efficiency.

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