Random Fractals and the Stock Market

Surrogates of the Stock Market - Cartoon Driven IFS

Equal Weight 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. The bin boundaries are set so bin1, bin2, bin3, and bin4 contain about the same number of data points. Here is the IFS driven by these differences as data points. As expected, squares 1, 2, 3, and 4 have about the same number of IFS points. There is a visible clustering of IFS points along the diagonal from (0,1) to (1,0) (data points hop between bin2 and bin3 in all combinations), and along the antidiagonal from (0,0) to (1,1) (data points hop between bin1 and bin4 in all combinations).

Return to equal weight bins.