The financial markets have now become more closely  interlinked in the world over than ever before despite  the differences in risk perceptions of the markets or the  country profiles. The dynamics of cross-country trade  and payments have evolved to such an extent that the  economic slowdown of a country is bound to affect its  trading partners as is clearly discernable from the  leading movement in the global stock prices. In the  current context of globalization and the subsequent  integration of the global markets, this study captures  the trends, similarities and patterns in the activities  and movements of the National Stock Exchange of  India (NSE) in comparison to the New York Stock  Exchange (NYSE). The prime objective of the study is to  check the long term association and cause & effect  relationship between the indices of Indian stock market  and New York Stock Exchange. Johansen's co integration test and Granger Wald Causality test are  used for examining the long term relationship between  both the stock markets, and to know the cause and effect  relationship between the variables selected. The  GARCH (1,1) model has been used to capture the main  characteristics of financial time series such as  stationarity, fat-tails, and volatility clustering. The  paper tests the correlation between the two exchanges  to prove that the Indian markets have become more  integrated with their global counterparts and their  reactions are in tandem with what are seen globally.