Migration Motif: A Spatial-Temporal Pattern Mining Approach for Financial Markets Xiaoxi Du, Ruoming Jin, Liang Ding, Victor E. Lee, John H.Thornton Jr Presented by: Xiaoxi Du Department of Computer Science Kent State University

Do we yet fully understand financial market risks? To describe frequent behaviors of individual companies To describe the relationships between stock market change over time and stock return

Example: Trajectories on a Financial Grid Financial Grid SIZE market captalization = (share price×number of shares) P/B Price-to-book ratio = (Current price per share / book value per share) Company Trajectory Compact Trajectory

T2 T1 10 Spatial and Temporal Constraint SIZESIZE P/B Spatial Constraint: To guaranteed to follow a bounded path U Temporal Constraint: An upper bound time constraint (short-term) ε

Migration Motif A migration motif (pattern) corresponds to a collection of sub-trajectories which follow similar path. properties:  pair-wise similarity: distance ≤ ε  Maximal: add one other sub-trajectory violate pair- wise similarity  Frequent: sub-trajectories → at least θ different trajectories

Algorithm Goal: To Extract Migration Motifs efficiently Trajectories (company) 2-Length Sub-Trajectories Similarity Graph Frequent 2-Length Migration Motif Frequent K-Length Migration Motif Apriori Property Compact Trajectory Pattern representation Graph theoretical Maximal Clique

Characteristics of the Datasets Data Source The Center for Research in Security Prices (CRSP) and Compustat Databases Time Period1964 to 2007 ParametersTemporal Constraint U = {3,4,5} Spatial Constraintε = {0,1,2} Minimum Support Level θ = {10,15,20} Grid Dimensionsg = {10×10, 20x20, 50x50, 100x100} Stock Exchanges and Description NYSE1717 (relatively large) NASDAQ2675 (smaller) AMEX825 (mostly smaller)

Motif Sensitivity to Parameters NYSE Motifs: (10g/U3/ε1/θ10)NYSE Motifs: (20g/U3/ε1/θ10) Result: NYSE

Motif Sensitivity to Parameters NASDAQ Motifs: (50g/U3/ε1/θ10) Result: NASDAQ

The randomized data contains many 2-length motif (M 2 ), Statistical Significance of Motifs However, random motifs longer than 2 are quite rare Risk factor migration in the stock market is not random, And should not be neglected

Oscillation Motif Patterns NYSE Motifs: (10g/U3/ε1/θ10) Value oscillation (horizontal) size oscillation (vertical)

Distribution of Motifs NYSE Motifs: (10g/U3/ε1/θ10) NASDAQ Motifs: (50g/U3/ε1/θ10)

Motif Timing - Average Starting Time - the point at which its migration pattern is first captured by a motif - Maturity - Average Staying Time - Long term vs Short term - Loser and Winners Portfolios

Motif Company Time Span - To list Membership information for typical motifs. -To provide each company’s ticker and time span - M5-45 time spans are highly concentrated for value oscillation path - M6-1 significant jumps - M4-50 no clear clustering of starting years for vertical oscillation path

Conclusion We introduce two new algorithms to discover migration motifs in the financial grid Our work is the first attempt to find multi-year migration patterns in financial datasets We are the first to find long oscillation patterns in P/B value