1. A Novel Method for Watching Economical Circulations Visualization of Economical Data via Mathematica Toshihiro Iwata *) yamana@res.kutc.kansai-u.ac.jp Kansai University *) T. Iwata, Scientific Analysis on Economic Fluctuation 2006 (Gakubunsha publ., in Japanese)

2. 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.

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 is the original data × × × × Now we stand t3.

5. 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.

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

7. moving slope analysis* By making 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

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

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

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

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

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

13. y-zx-zx-y 3D-plot Gallery III Hitachi Shipbuilding

14. Behavior of Moving Slope Repeatedly The values become smaller step by step. Original Data Moving Slope at One Time Moving Slope at Two Time Moving Slope at Three Time Moving Slope at Four Time ellipse

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 k 2 sin kx f'''(x) = - A k 3 cos kx 0<k<1, is a fixed number and A is an amplitude. We think next model function (at k 1 < k 2 < …< kn …< 1). T(t) = A 1 sin k 1 t - j 1 + A 2 sin ( k 2 t - j 2 ) … + An sin ( k n t - j n ) … So we can propose next general solution. u(t) = A 1 sin k 1 t - j 1 + A 2 sin ( k 2 t - j 2 ) …+ 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 Z

16. 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 highly correlated. My new book : Scientific Analysis on Economic Fluctuation 2006 (in Japanese) Than