Driven IFS and Financial Cartoons

Sample

Suppose we moved the first turning point, say to (x1, y1) = (2/9, 2/3).

Will this driven IFS match the data driven IFS?

Here are the time series, differences, and driven IFS with B2 = 0 and B1 and B3 one-half of the maximum distance from B2.

Most of the driven IFS points lie along the diagonal.

Looking at the difference graph, this is no surprise, because almost all the differences lie in bin 2 and bin 3.

Here are the differences and driven IFS with B2 = 0 and B1 and B3 one-fifth of the maximum distance B2.

This is not a good match to the data, primarily because the antidiagonal squares 11, 14, 41 and 44 are much more heavily populated than they are in the data driven IFS.

Based on these observations, it appears that the first choice of turning point, (x1, y1) = (1/3, 2/3), gives a better match to the data than does the second, (x1, y1) = (2/9}, 2/3).

To be sure, we should experiment with different placements of B1 and B3 before drawing any conclusion.

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