Random Fractals and the Stock Market

Surrogates of the Stock Market - Cartoon Driven IFS

Equal-Size Bins - Example 2

Here we use the cartoon with generator having turning points (2/9, 2/3) and (5/9, 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 and very few in bin₁, bin₃, and bin₄. Here is the IFS driven by these differences as data points. Most of the IFS points cluster near (1,0), the result of most of the data points lying in bin₂. Along the bottom of the square, note the clusters of IFS points at (1/2,0), (3/4,0), (7/8,0), and (15/16,0). Almost all the IFS points along the bottom of the square lie in these clusters, indicating that a long sequence of data points in bin₂ can be followed by a single data point in bin₁, followed immediately by more data points in bin₂. The less clustered distribution of IFS points along the line between (1,0) and (0,1) indicates that data points fall in bin₂ and bin₃ in more complicated combinations.

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 and very few in bin₁, bin₃, and bin₄.	Here is the IFS driven by these differences as data points. Most of the IFS points cluster near (1,0), the result of most of the data points lying in bin₂. Along the bottom of the square, note the clusters of IFS points at (1/2,0), (3/4,0), (7/8,0), and (15/16,0). Almost all the IFS points along the bottom of the square lie in these clusters, indicating that a long sequence of data points in bin₂ can be followed by a single data point in bin₁, followed immediately by more data points in bin₂. The less clustered distribution of IFS points along the line between (1,0) and (0,1) indicates that data points fall in bin₂ and bin₃ in more complicated combinations.