Driven IFS and Data Analysis

Driven IFS and the Taiwanese and Chinese Stock Markets

In his project for the autumn, 2000, fractal geometry course, Enoch Wu used driven IFS to compare the Taiwan stock market (TAIEX) and the Shanghai Securities Exchange (SSE). Wu proposed a novel application of IFS:

if both markets rise, apply T1(x,y) = (x/2,y/2), if TAIEX falls and SSE rises, apply T2(x,y) = (x/2,y/2) + (1/2,0), if TAIEX rises and SSE falls, apply T3(x,y) = (x/2,y/2) + (0,1/2), and If both markets fall, apply T4(x,y) = (x/2,y/2) + (1/2,1/2).

That is, in relation to the driven IFS

If the markets generally move together, we should see many applications of T1 and T4, thus many points lying along the diagonal from lower left to upper right.

On the left is the driven IFS for the Dow Jones and NASDAQ, from July 3, 1997 to December 1, 2000, a total of 861 data points. On the right, the driven IFS for the TAIEX and the SSE.

Indeed, we see a strong trend along this diagonal for the DJIA and NASDAQ, not so strong for the TAIEX and the SSE.

Disappointed with the absence of a strong pattern in the TAIEX/SSE plot, Wu divided the data at May 22, 2000, the inauguration of Taiwan's new president. Next, Wu analyzed the individual markets. Finally, an observation about lags between movements of the markets.

Return to IFS Driven by Financial Data.