Driven IFS and Data Analysis

Traditional and Driven IFS Correlations

In their project for the autumn, 2000, fractal geometry course, Simo Kalla and Nader Sobhan analyzed the differences in daily closing prices of six stocks for the 251 trading days in 1998. They selected

Coca-Cola and Kellogg (food industry), Nokia and Motorola (telecommunications), Microsoft (software), and Chase Manhattan (banking).

Dow Jones Interactive was the source of the information. Here are the driven IFS plots.

Coca-Cola Kellogg Nokia Motorola Microsoft Chase Manhattan

First, we compute the standard statistical correlations of the data. Comparing the driven IFS for the pair with the highest correlation, we find some discrepancies. Next, we comapre the number of points in each Length 2 address square of the driven IFS. Finally, we define a correlation based on length 2 address populations.

This was a small test, a small number of stocks and only one year's data.

Moreover, comparing only the length two addresses is fairly crude.

With more data, longer address squares could be compared, giving more refined measurements of the relative motions of the stocks.

Nevertheless, this is a clever idea.

Kalla and Sobhan conclude, "Since fractal geometry is a relatively new field, it might open doors to exciting new ways of measuring correlations of two random variables."

Return to IFS Driven by Financial Data.