Random Fractals and the Stock Market

Surrogates of the Stock Market - Cartoon Driven IFS

Mean-Centered Bins - Example 3

Here we use the cartoon with generator having turning points (1/9, 2/3) and (5/9, 1/3).

Here are the successive differences of the cartoon data, where B1 and B3 are 0.1σ from the mean. Note most differences lie in bin1 and bin4; it appears that few in bin2 and bin3 because these bins cover such a small range. Here is the IFS driven by these differences as data points. The most visible features are (i) most IFS points lie on the line connecting the lower left and upper right corners of the square, and (ii) a noticeable number of IFS points lie on the line connecting the lower right and upper left corners of the square. Evidently, bin2 and bin3 contain do contain a fair number of points that occur in many combinations (though not all - do you see some gaps along this line? What are the addresses of the empty regions?

To illustrate the extent to which the details of this driven IFS depend on the distance A from B1 and B3 to B2, in this animation we let A change from 0.5σ to 3.0σ, in steps of 0.5σ.

Click the picture to animate.

Return to Mean-centered bins.