Fractal Analysis of S&P 500 Sector Indexes

Abstract

In this study multifractal properties of S&P 500 sector indexes are investigated with Multifractal Detrended Fluctuation Analysis (MF-DFA). The MF-DFA is a signal processing technique that is used to describe the multifractal properties of a time series data. It is an extension of Detrended Fluctuation Analysis (DFA), which is a widely utilized method for estimating the scaling behavior of a time series. Main idea behind MF-DFA is to decompose a time series into multiple scales using a coarse-graining procedure, and then to estimate the scaling behavior of each scale using DFA. This gives a set of scaling exponents that describe the multifractal features of the time series. Our MF-DFA results indicates the presence of multifractality in all S&P 500 sector indexes. Since these indexes are multifractal, we can conclude that they possess properties such as scaling variability, nonlinear dynamics, self-similarity, long-range dependence, multiscale correlations and nonstationary.