A methodology to create statistical arbitrage in stock Index S&P500 is presented. A synthetic asset based on the cointegration relationship of the stocks with Index was constructed. In order to capture the dynamic of the market time adaptive algorithms have been developed and discussed. The pair trading strategy was applied in different periods between S&P500 and synthetic asset and the results were evaluated. Different metrics have shown that the Multvariate Kalman Algorithm creates statistical arbitrage in index with much lower Maximum Drawdown and higher profit. The algorithm is neutral as the beta is close to zero and the Sharp Ratio remains high in all cases.