Random Fractals and the Stock Market

Surrogates of the Stock Market - Cartoon Driven IFS

Equal-Size Bins - Example 3

Here we use the cartoon with generator having turning points (3/9, 2/3) and (6/9, 1/3).

Here is the time series of the cartoon data. Here is the IFS driven by the data. Note the familiar backward Z, a characteristic of consecutive data points lying in the same bin or in adjoining bins.

Here are the successive differences of the cartoon data. Note most differences lie in bin₂, some in bin₁, and very few in bin₃ and bin₄. Here is the IFS driven by these differences as data points. The bulk of the IFS points lie in square 2, as expected. The bottom of the square is mostly filled in, except for the left-most part (square 111, indicating three consecutive data points do not lie in bin₁) and the images (2111, 22111, and 222111 are visible) of that gap along the bottom of the square.

Return to equal-size bins.


Here is the time series of the cartoon data.	Here is the IFS driven by the data. Note the familiar backward Z, a characteristic of consecutive data points lying in the same bin or in adjoining bins.

Here are the successive differences of the cartoon data. Note most differences lie in bin₂, some in bin₁, and very few in bin₃ and bin₄.	Here is the IFS driven by these differences as data points. The bulk of the IFS points lie in square 2, as expected. The bottom of the square is mostly filled in, except for the left-most part (square 111, indicating three consecutive data points do not lie in bin₁) and the images (2111, 22111, and 222111 are visible) of that gap along the bottom of the square.