Leadership Ranking: Bringing Order to Correlated Time Series

Data streams have emerged as an important research area in recent years due to its ubiquitous presence in various application domains including stock market analysis in finance. Therefore, it has become increasingly demanding to develop efficient techniques to discover useful patterns from such data streams. Among many issues, analyzing the correlation between two data streams is an important technique to study linear co-movements of two data streams [11, 9]. Yet, lagged correlation further captures lagged co-movements between time-evolving streams [4, 6], which is especially useful for forecasting and monitoring. In empirical finance, the statistics (e.g., price, return, volatility) of a security may exhibit a lead-lag effect on those of other securities [7]. This information can be used to predict the trends of the led securities. Although the lagged correlation between a pair of streams has been well studied in empirical research [3, 1] and efficient algorithms to discover lagged correlations have also been developed [8], the study on analyzing the relationships across multiple data streams is still lacking. The comprehensive relationships among multiple data streams is very helpful in understanding, monitoring and controlling the overall movement of the entity where the data streams are generated. We study the problem of discovering the leadership relationships among a set of time series by analyzing lead-lag relations. In particular, we study this problem on one of its typical applications in financial market: finding the leaders among multiple time series of stock prices. Extracting the group of stock leaders will bring enlightening information as discussed below.