Random Fractals and the Stock Market

Surrogates of the Stock Market - Cartoon Driven IFS

Equal Weight Bins

Here we use equal weight bins to drive the IFS with data generated by several cartoons.

For later comparison with some financial data sets, we take cartoons with 3128 data points.

Recall the generator for Brownian motion has turning points (4/9,2/3) and (5/9,1/3). A small departure from Brownian motion is the generator with turning points (1/3,2/3) and (5/9,1/3). Here is an example. Next we consider the generator with turning points (2/9,2/3) and (5/9,1/3). Here is an example. As expected, the departures from Brownian motion are even more pronounced. Next we consider the symmetric generator with turning points (1/3,2/3) and (2/3,1/3). Here is an example. Finally, we consider the symmetric generator with turning points (2/9,2/3) and (7/9,1/3). Here is an example.

A comparison of these driven IFS shows equal weight bins reveal little patterns, other than the clustering along the diagonal and antidiagonal, becoming more pronounced as the generator departs farther from Brownian.

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