Price correlation 을 을을을 을을 을을을을 을을을 clustering 을을을 Seung-Woo Son email: [email protected] Complex System and Statistical Physics Lab., Dept. Physics, KAIST, Taejeon 305-701, Korea 2003. 12. 13. SERI
Jan 05, 2016
Price correlation 을 이용한 경제네트워크 구성과 clustering 가능성
Seung-Woo Son email: [email protected]
Complex System and Statistical Physics Lab., Dept. Physics, KAIST, Taejeon 305-701, Korea
2003. 12. 13. SERI
Correlation ?
Price correlation vs. Return correlation
T/N ratio ( T: trading day, N: number of companies )
– random matrix theorem – should be significantly larger than one
Correlation matrix vs. Distance matrix )1(2 ,, jiji cd
Price correlation
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.000
0.001
0.002
0.003
0.004
Dis
trib
utio
n
Correlation Value
1991 - 2003 ( 468 companies, 3431 trading days )
Log return correlation
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.000
0.001
0.002
0.003
0.004
Dis
trib
utio
n
Correlation Value
1991 - 2003 ( 468 companies, 3431 trading days )
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.000
0.002
0.004
0.006
0.008
Dis
trib
utio
n
Correlation value
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.00.000
0.002
0.004
0.006
0.008
Dis
trib
utio
n
Correlation value
1980 - 2003 ( 228 companies, 6648 trading days )
Price log return
Correlation between two correlations
1991 - 2003 ( 468 companies, 3431 trading days )
1 10 100
1
10
100
Dis
trib
utio
n
degree
MST - Price correlation
1991 - 2003 ( 468 companies, 3431 trading days )
1 10 100
1
10
100
~ 2.076
Dis
trib
utio
n o
f d
eg
ree
degree (k)
MST - Return correlation
1991 - 2003 ( 468 companies, 3431 trading days )
Time moving of return correlation
Period -1982~2000
NYSE105 comp.
Black Monday( 1987 )
Dong-Hee Kim
1982~1986, IBM k=24
1983~1987, GE k=34
1985~1989, GE k=27
1986~1990, GE k=25
1993~1997, MER k=16
1996~2000, GE k=23
Percolation approach &Girvan-Newman cluster method
After sorting Cij in descending order, add a link between i and j following that order. When all nodes make a giant cluster, stop the attachment.
It means the links with values Cij > C * (percolation threshold) are valid and connected.
1.Building giant cluster by percolation approach
2.Break into several cluster by Girvan-Newman cluster method
1991 - 2003 ( 468 companies, 3431 trading days )
Percolate net (all node connected condition) 468 nodes, 85376 links (78.13% of fully connected) bad case!!
- meaningless degree distribution
1991 - 2003 ( 468 companies, 3431 trading days )
Hierarchical tree – clustering
average link method– 두 cluster 사이에 평균 거리 순으로 연결
complete link method– 두 cluster 사이에 가장 먼 거리 순으로…
single link method– 두 cluster 사이에 가장 가까운 거리 순으로…
single link method 는 MST 방법과 일치
average link method
Young-Ho Eom
1991 - 2003 ( 468 companies, 3431 trading days )
complete link method
Young-Ho Eom
1991 - 2003 ( 468 companies, 3431 trading days )
single link method
Young-Ho Eom
1991 - 2003 ( 468 companies, 3431 trading days )
Conclusion
한국증시 KOSPI
Detailed list of used data