Random Fractals and the Stock Market

Surrogates of the Stock Market - Cartoon Driven IFS

Zero-Centered Bins - Example 1

Here we use the cartoon with generator having turning points (3/9, 2/3) and (5/9, 1/3). The bin boundary B2 is set to 0, and B1 and B3 are one-quarter of the range below and above B2.

Here are the successive differences of the cartoon data. Note most differences lie in bin2 and bin3, few in bin1 and bin4. Here is the IFS driven by these differences as data points. Most of the IFS points cluster along the diagonal between (1,0) and (0,1) Note also the faint subdiagonal (between (1/2,0) and (0,1/2)) and superdiagonal (between (1,1/2) and (1/2,1)) echoes of the diagonal. These indicate that some, but not all, combinations of 2 and 3 can be followed by 1 and by 4.

Return to zero-centered bins.