Embed Size (px)
Citation preview
A Novel Method for Watching Economical Circulations
Visualization of Economical Data via Mathe
matica
Toshihiro Iwata *)
Kansai University
*) T. Iwata,Scientific Analysis on Economic Fluctuation
2006 (Gakubunsha publ., in Japanese)
Points of view in this report
1 Regression analysis are ambiguous and not helpful for chaotic phenomenon.
2 Chaotic analysis must be in positive approach essentially.
3 On two components of complexity and circulation（ spectrum and moving slope） live together.
By taking a moving slope in the stock, we can find out the regularity of the stock
fluctuation of above case.
• The moving slope is a useful tool in cases where it is difficult to find the points of change like the peak or bottom in the source data.
• This has the nature of possible subrogation to differential coefficients, and the next time instant can show in which direction and with how much force a movement is. The formula of moving slope Xt’ of the term 2P+1 is as follows.
• Xt=[ － PXt-p － ... － 2Xt-2 － 1Xt-1+1Xt+1+2Xt+2+...+PXt+p] ÷ [P(P+1)(2P+1)/3]
• For example, the moving slope Xt’ of the term 5 can be expressed as the next formula.
• Xt=[ － 2Xt-2 － 1Xt-1+1Xt+1+2Xt+2] ÷10
We consider the structure of the moving slope Xt’ of the term 5.
• Xt=[ － 2Xt-2 － 1Xt-1+1Xt+1+2Xt+2] ÷10 ・
・ ・ １ ２ ３ ４ ５
・
・ ・ is the original data
ｔ× （－２）
× （－１）
× （＋１）
× （＋２）
Now we stand t3.
Every Stock Prices are Random When it shows regularities such as a cycle by time change of this
moving slope, the forecast to the quality near 1/f is better. The forecast that we can get by these two analyses are completely our original one.
（２０００．１－２００６．４ ）
Stock Price of Sony 1983.1- 2006.5
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
1 15 29 43 57 71 85 99 113 127 141 155 169 183 197 211 225 239 253 267
month
By making Fourier transformFourier transform,
Ex) Sony co.
Many frequencies inside
No specific dominant frequency inside …
NOTE
Fourier analysis
spectrum of sony stock prices
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
- 3 - 2.5 - 2 - 1.5 - 1 - 0.5 0
frequency
pow
er(
log)
By making moving slope analysis*moving slope analysis*,
Ex) Sony co.
Many frequencies make an collective circulation.
It is a complicated motion (but it is confined in “circulations”)
NOTE
Moving slope analysis
-500-250
0250
500
-100
0
100
200
-100
-50
0
50
100
-500-250
0250
500
-100
0
100
200
Limited motion
complexity
Unpredictable factor(Predictable-like)
Here, we can see two components …
circulation
Model solution and x-y, y-z and x-z plot
y-z x-z x-y
We can find a thin film structure for x-z plot !!
-2000
200
400
-100
0
100
200
-50
0
50
100
-2000
200
400
-100
0
100
200
-2000200400
-1000100200
-50
0
50
100
-50
0
50
100
-200 0 200 400
-1000
100200
-50
0
50
100
-200 0 200 400
-200 0 200 400
-100
0
100
200
-50
050100 -100
0
100
200
New York Dow
y-z x-z x-y
-1000
0
1000
-250
0
250500
-200
-100
0
100
200
-1000
0
1000
-250
0
250500
-1000
01000
-2500250500
-200
-100
0
100
200
-200
-100
0
100
200
-1000 0 1000
-2500
250500
-200
-100
0
100
200
-1000 0 1000
-1000 0 1000
-250
0
250
500-200
-1000
100200
-250
0
250
500
Average Stock Price of Japan
3D-plot Gallery I3D-plot Gallery I
-100
0
100
-50
0
50
-40
-20
0
20
-100
0
100
-50
0
50
-1000100
-50050
-40
-20
0
20
-40
-20
0
20
-100 0 100
-50
050
-40
-20
0
20
-100 0 100
-100 0 100
-50
0
50
-40
-20020
-50
0
50
y － z x－ｚ ｘ－ y
Kojima
y-z x-z x-y
3D-plot Gallery 3D-plot Gallery IIII
-100
0
100
-50
0
50
-40
-20
0
20
-100
0
100
-50
0
50
-1000100
-50050
-40
-20
0
20
-40
-20
0
20
-100 0 100
-50
050
-40
-20
0
20
-100 0 100
-100 0 100
-50
0
50
-40
-20020
-50
0
50
Dainippon Printing
y-z x-z x-y
3D-plot Gallery III3D-plot Gallery III
-100
0
100
-50
0
50
-40
-20
0
20
-100
0
100
-50
0
50
-1000100
-50050
-40
-20
0
20
-40
-20
0
20
-100 0 100
-50
050
-40
-20
0
20
-100 0 100
-100 0 100
-50
0
50
-40
-20020
-50
0
50
Hitachi Shipbuilding
Behavior of Moving Slope RepeatedlyThe values become smaller step by step.
Original Data
Moving Slope at One Time
Moving Slope at One Time
Moving Slope at Two Time ｓ
Moving Slope at Two Time ｓ
Moving Slope at Three Time ｓ
Moving Slope at Three Time ｓ
Moving Slope at Four Time ｓ
ellipse
Model solution and x-y, y-z and x-z plot
f(x) = A sin kx f'(x) = A k cos kx f''(x) = - A k2 sin kx f'''(x) = - A k3 cos kx
0<k<1 , ｋ is a fixed number and A is an amplitude.
We think next model function (at k1 < k2 < …< kn …< 1).
T(t) = A1 sin （ k1 t - j1 ） + A2 sin ( k2 t - j2) … + An sin ( kn t - jn) …
So we can propose next general solution.
u(t) = A1 sin （ k1 t - j1 ） + A2 sin ( k2 t - j2) …+ An sin ( kn t - jn) + …
jn : fixed
This solution is based on the fact that j component does not drastically depend on time.
NOTE
New York Dow
Ｘ－ Z
-200 0 200 400
-1000
100200
-50
0
50
100
-200 0 200 400
Summary & Perspective
The complicated evolution seems to be circulating in a limited finite box (it seems to have some rules). Our opinion is that such limited circulation and complexity are hig
hly correlated.
My new book : Scientific Analysis on Economic Fluctuation
2006 (in Japanese)
Than ｋｓ！
