1. Characterizing Stock Market Behavior Correlations in Complex Networks
Daniel Lopez
CS – 765
Fall 2017

2. Brief Overview Review of Problem Methodology
Bipartite Graphs and Projections
Temporal shifts in correlation
Expected Results and Comparisons

3. Review
Stock tickers are represented as nodes in the graphs, and the edges between them represent similarities between graphs.

4. Goal and Motivation
What is the best way to define that correlation such that similar stocks are more linked together? How can we characterize temporal causality behavior in this way? To maximize portfolio diversity (for loss resiliency), you want stocks that have a large average path length. I want to generalize this to any set of multiple stochastic time series value whose behavior you want to quantify.

5. Methodology

6. Bipartite Graph
First, let’s represent a set of portfolios that buy and sell stocks in a resulting bipartite graph. Each portfolio randomly buys and sells stock at different intervals with the only condition that whichever action they take, it’s applied to ALL stocks.

7. Bipartite Graph
When these portfolios buy their stock, they will buy whatever is $100 of it (for normalization purposes). Behavioral characterization should tend to give more positively correlated trends values closer to 1 and more negatively correlated trends closer to -1

8. Bipartite Graph with Time Shifts
To consider causality between portfolios after some time shift, we have a copy of the portfolios which according to their unique variable, the phase shift 𝛿, will focus on a particular portfolio. For a set of portfolios with a time-shift, their results would provide a temporal shift in the weight of the projections, showing temporal causality.
Time step: 1 2 3 4 5 6 7 8
Action
Buy
Single
Buy the Rest
Sell Single
Sell
Rest

9. Bipartite Graph with Time Shifts
We will be varying the time shift, and having a set of portfolios that focus on each stock respectively. Notice the dashed line which implies that it will perform the action on these stocks later in time.

10. Equation for correlation
Let 𝑓 𝑝 𝑖 =∑ ln 𝑠∈S 𝑠(𝑡+𝑑) 𝑠(𝑡) , which stands for the return for portfolio pi who bought at time t and sold at time t+d. Consider a correlation matrix, where the values are defined as 𝑒 𝑖𝑗 = 𝑝∈𝑃 2(𝑓 𝑝 𝑖 +𝑓( 𝑝 𝑗 )) 𝑓 𝑝 𝑖 +|𝑓 𝑝 𝑗 | −1
Denominator normalizes to 0 and 1, multiplying by 2, and subtracting 1 puts in range [-1,1]

11. How To Interpret Results

12. Comparing Results
Since we are varying deltas and stock focuses, we will produce graphs that show different metrics of the one mode projection.
PageRank or Density -> Influence of Stock
Clustering -> High stock similarity behavior
Path Length -> Strength of Influence
Centrality -> Most important stocks
We will be comparing using Pearson Correlation for these values, and see which better captures different characteristics.
Denominator normalizes to 0 and 1, multiplying by 2, and subtracting 1 puts in range [-1,1]

13. Minimum Spanning Tree
There are papers were the countries themselves are considered nodes and the financial transactions between economic systems are considered for edges.

14. Future Work
We could use other economical stock properties than just the price of the stock; maybe the DEMA, TEMA, T3 metrics as data points. Instead of performing actions randomly for a different amount of time, the actions could be periodic and pattern based.

15. References
[1] Grigory A. Bautin, Valery A. Kalyagin, Alexander P. Koldanov, Petr A. Koldanov, and Panos M. Pardalos. Simple measure of similarity for the market graph construction. Computational Management Science, 10(2):105–124, Jun [2] You-Min Ha, Sanghyun Park, Sang-Wook Kim, Jung-Im Won, and Jee- Hee Yoon. A stock recommendation system exploiting rule discovery in stock databases. Information and Software Technology, 51(7):1140 – 1149, Special Section: Software Engineering for Secure Systems. [3] Wang Sen Lan, Guo Hao Zhao, and Li Jun Hou. Stocks network analysis based on visualization. In Intelligent Structure and Vibration Control, volume 50 of Applied Mechanics and Materials, pages 323–327. Trans Tech Publications, [4] R. N. Mantegna. Hierarchical structure in financial markets. The European Physical Journal B - Condensed Matter and Complex Systems,11(1):193–197, Sep [5] Preeti Paranjape-Voditel and Umesh Deshpande. A stock market portfolio recommender system based on associate rule mining. Applied Soft Computing, 13: , Mar [6] Chi K. Tse, Jing Liu, and Francis C.M. Lau. A network perspective of the stock market. Journal of Empirical Finance, 17(4):659–667, September 2010

16. Thank you for listening
Q&A
Any questions?