Points of view in this report

1. A Novel Method for Watching Economical Circulations Visualization of Economical Data viaMathematicaToshihiro Iwata *)yamana@res.kutc.kansai-u.ac.jp Kansai University*) T. Iwata,Scientific Analysis on Economic Fluctuation2006 (Gakubunsha publ., in Japanese)

2. Points of view in this report 1 Regression analysis are ambiguous and not helpfulfor 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.

3. 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

4. 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 ×（－１） ×（＋１） ×（－２） ×（＋２） Now we stand t3.

5. Every Stock Prices are RandomWhen 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　）

6. Fourier analysis Ex) Sony co. By makingFourier transform, NOTE • Many frequencies inside • No specific dominant frequency inside …

7. Moving slope analysis By makingmoving slope analysis*, Ex) Sonyco. NOTE • Many frequencies make an collective circulation. • It is a complicated motion (but it is confined in “circulations”)

8. Here, we can see two components … circulation complexity Limited motion Unpredictable factor (Predictable-like)

9. Model solution and x-y, y-z and x-z plot New York Dow y-z x-z x-y • We can find a thin film structure for x-z plot !!

10. Average Stock Price of Japan y-z x-z x-y

11. 3D-plot Gallery I Kojima y－z ｘ－y x－ｚ

12. 3D-plot Gallery II Dainippon Printing y-z x-y x-z

13. 3D-plot Gallery III Hitachi Shipbuilding y-z x-z x-y

14. 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 Timeｓ Moving Slope at Two Timeｓ Moving Slope at Three Timeｓ ellipse Moving Slope at Three Timeｓ Moving Slope at Four Timeｓ

15. 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 generalsolution. u(t) =  A1 sin（k1 t - j1 ）  + A2 sin ( k2 t - j2)  …+ An sin ( kn  t - jn) + …jn:fixed New York Dow Ｘ－Z NOTE • This solution is based on the fact that j component does not drastically depend on time.

16. Summary & PerspectiveThe 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 highly correlated.My new book : Scientific Analysis on Economic Fluctuation2006 (in Japanese)Thanｋｓ！