5. Random Fractals and the Stock Market

5.J. Random Fractal Cartoons and Stock Market Models

Much real data appears to exhibit both global dependence and long tails.

To prepare for developing random mathematical processes with both properties, we introduce a very simple method of synthesizing Brownian motion.

Next, we modify this method to produce global dependence (unifractal cartoons) and then both global dependence and long tails (multifractal cartoons).

We conclude by restricting our attention to symmetric cartoons, and illustrate the variety of behaviors that arise in this restricted situation.

First, we present the basic construction of the cartoons. As a simple application, we show how to simulate Brownian motion using simple cartoons. Next, we modify the cartoon generator to more general unifractal cartoons, incorporating global dependence. Then, we modify the cartoon generator to still more general multifractal cartoons, incorporating both global dependence and long tails. Next, we specialize the cartoon generator to symmetric cartoons, and illustrate the wide range of behaviors that occur in even this restricted situation. Return to Random Fractals.