Random Fractals and the Stock Market

Surrogates of the Stock Market - Cartoon Driven IFS

Equal-Size Bins

Here we use equal-size 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 the driven IFS shows that as the generator departs more from Brownian, the driven IFS with equal size bins reveal less useful patterns.

Return to Cartoon Driven IFS.