AbstractFinancial markets are the outcome of highly complex interactions among a number of agents. Such a complex system possibly contains all sorts of features, e.g., not only static but also dynamic. Here we study dynamic correlations hidden in the S&P 500 market by adopting a combined method of the Complex Principal Component Analysis (CPCA) and the Random Matrix Theory (RMT). The CPCA is entirely dependent on complexification of time series using the Hilbert transformation and enables us to extract correlations between stock prices moving with different phases to one another. The RMT serves as a null hypothesis for distinguishing true correlations from noisy financial data. The extracted information on dynamic correlations of the market is projected onto a correlation network in which pairs of stocks with phase difference smaller than certain threshold are linked with strength of their correlations as weight. We then detect communities of comoving stocks in the network and also elucidate lead-lag relationship between those communities.