migration motif: a spatial-temporal pattern mining approach for financial markets xiaoxi du, ruoming...
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Migration Motif: A Spatial-Temporal Pattern Mining
Approach for Financial MarketsXiaoxi Du, Ruoming Jin, Liang Ding, Victor E. Lee, John H.Thornton Jr
Presented by: Xiaoxi Du
Department of Computer ScienceKent State University
Do we yet fully understand financial market risks?
To describe frequent behaviors
of individual companies
To describethe relationships
between stock market change over time and
stock return
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8
P/B
SIZE
9 10
SBUX
2
24
3
GT3
2
SJM
6
3
5
WEC
PU
2
2
2
4
2
5
SJM:SMUCKER
J M CO
GT:GOODYEAR
YIRE&
RUBRCO
SBUX:STARBUCKS
CORP
PU:PULLMAN
INC
WEC:WISCONSIN
ENERGYCORP
Example: Trajectories on a Financial Grid
Financial Grid
SIZEmarket captalization
= (share price×number of shares)
P/BPrice-to-book ratio
= (Current price per share / book value per share)
Company Trajectory
Compact Trajectory
1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
T2
T1
10
10
Spatial and Temporal Constraint
SIZE
P/BSpatial Constraint:
To guaranteedto follow
a bounded pathU
Temporal Constraint:An upper boundtime 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
AlgorithmGoal:To Extract
Migration Motifsefficiently
Trajectories(company)
2-LengthSub-Trajectories
Similarity GraphFrequent 2-Length
Migration Motif
FrequentK-Length
Migration Motif
AprioriProperty
CompactTrajectory
Patternrepresentation Graph
theoretical
MaximalClique
Characteristics of the Datasets
Data Source The Center for Research in Security Prices
(CRSP) and Compustat Databases
Time Period 1964 to 2007
Parameters Temporal Constraint
U = {3,4,5}
Spatial Constraint ε = {0,1,2}
Minimum Support Level
θ = {10,15,20}
Grid Dimensions g = {10×10, 20x20, 50x50, 100x100}
Stock Exchanges
andDescription
NYSE 1717 (relatively large)
NASDAQ 2675 (smaller)
AMEX 825 (mostly smaller)
Motif Sensitivity to Parameters
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8
P/B
SIZE
M6-1
M5-59
M5-37
M5-58
M5-45
M5-25
9 10
NYSE Motifs: (10g/U3/ε1/θ10)
17
P/B
SIZE
M5-6
20
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1 191817161514131211
1
2
M5-13
M5-10
M5-16 M5-2
3 4 5 6 7 8 9 10
18
19
20
M3-42
M4-186
M3-433
M4-184
M4-101
M3-115
NYSE Motifs: (20g/U3/ε1/θ10)
Result: NYSE
Motif Sensitivity to Parameters
50
P/B
SIZE
21
...
4
3
2
1 1916151211
1
... ... ... ... ... 23 ... 25 ... 28 ... 49M6-2M5-17
M5-3
5
6
M3-170M3-304
M3-172
50
M3-22
M4-50
NASDAQ Motifs: (50g/U3/ε1/θ10)
Result: NASDAQ
The randomized data contains many 2-length
motif (M2),
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
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8
P/B
SIZE
M6-1
M5-59
M5-37
M5-58
M5-45
M5-25
9 10
NYSE Motifs: (10g/U3/ε1/θ10)
Value oscillation(horizontal)
size oscillation(vertical)
Distribution of Motifs
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8
P/B
SIZE
M6-1
M5-59
M5-37
M5-58
M5-45
M5-25
9 10
NYSE Motifs: (10g/U3/ε1/θ10)
50
P/B
SIZE
21
...
4
3
2
1 1916151211
1
... ... ... ... ... 23 ... 25 ... 28 ... 49M6-2M5-17
M5-3
5
6
M3-170M3-304
M3-172
50
M3-22
M4-50
NASDAQ Motifs: (50g/U3/ε1/θ10)
Motif Timing
2 2 23 3 3 44 4 55 5 66 60
5
10
15
20
25
NYSE10×10 NASDAQ50×50 AMEX50×50
Motifs by Length and by Market
Ave
rage
Sta
rtin
g Y
ear
- 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