Migration Motif: A Spatial-Temporal Pattern Mining Approach for Financial Markets

A recent study by two prominent finance researchers, Fama and French, introduces a new framework for studying risk vs. return: the migration of stocks across size-value portfolio space. Given the financial events of 2008, this first attempt to disentangle the relationships between migration behavior and stock returns is especially timely. Their work, however, derives results only for market segments, not individual companies, and only for one-year moves. Thus, we see a new challenge for financial data mining: how to capture and categorize the migration of individual companies, and how such behavior affects their returns. We propose a novel data mining approach to study the multi-year movement of individual companies. Specifically, we address the question: ``How does one discover frequent migration patterns in the stock market?'' We present a new trajectory mining algorithm to discover migration motifs in financial markets. Novel features of this algorithm are its handling of approximate pattern matching through a graph theoretical method, maximal clique identification, and incorporation of temporal and spatial constraints. We have performed a detailed study of the NASDAQ, NYSE, and AMEX stock markets, over a 43-year span. We successfully find migration motifs that confirm existing finance theories and other motifs that may lead to new financial models.