Date of Submission

Fall 2011

Academic Program

Mathematics

Project Advisor 1

Samuel Hsiao

Abstract/Artist's Statement

For the past few decades mathematicians and physicists have been paying more attention to fractals in nature, ways to analyze them and work with them. In particular, one of the main properties of such fractals, self-affinity has been studied extensively by a famous mathematician Mandelbrot. In this paper I am going to introduce the concept of the Hurst exponent, which is used to characterize the self-affinity of a fractal. This project is going to explain the idea of the Hurst exponent and compare different methods of estimating it, to see which method is more efficient. One of the methods was introduced very recently by Yuri Kuperin and has not yet been published. In the final chapter of my paper I am going to analyze real data and simulated data. Simulated data will be put through several experiments with different values of Hurst exponent assigned and different sizes of the data sets, to see what are the criteria for each method to give the best estimate. For the real data, the values of the Dow Jones Industrial Average will be used as an example of a natural fractal. I will try to interpret the results obtained from the real data analysis.

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