Random Fractals and the Stock Market

Surrogates of the Stock Market - Cartoon Driven IFS

We study IFS driven by several multifractal finance cartoons.

The goal is to investigate different binning schemes to find the best discriminator between the cartoons.

Then with this binning, we find cartoons that best match real data.

Examples of IFS driven by cartoons with equal-size bins. This is not particularly useful: for cartoons that differ much from Brownian, most IFS points cluster in one corner. Examples of IFS driven by cartoons with equal weight bins. Also not so useful: except for diagonal and antidiagonal clustering (stronger the more the cartoon differs from Brownian), little structure is visible. Examples of IFS driven by cartoons with bins centered at 0. Varying the bin width, as a fraction of the range of values, reveals changes in the driven IFS patterns for the differences. Examples of IFS driven by cartoons with bins centered at the mean, and width a multiple of the standard deviation. Comparison of IFS driven by cartoons and by data.

Return to Surrogates of the Stock Market.