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.

Keywords

• Multifractality
• MF-DFA
• Multifractal Detrended Fluctuation Analysis
• Fractal Theory
• S&P 500

S&P 500 Sektör Endekslerinin Fraktal Analizi

Abstract

Bu çalışmada S&P 500 sektör endekslerinin çoklu fraktal özellikleri Çoklu Fraktal Eğilimden Arındırılmış Dalgalanma Analizi (ÇF-EADA) ile incelenmiştir. ÇF-EADA zaman serisi verilerinin çoklu fraktal özelliklerini tarif etmek için kullanılan bir sinyal işleme tekniğidir. Bu yöntem zaman serilerinin ölçekleme davranışını tahmin etmek için kullanılan Eğilimden Arındırılmış Dalgalanma Analizi (EADA) yönteminin bir uzantısıdır. ÇF-EADA yönteminin arkasında yatan temel fikir bir zaman serisini kaba ölçekli bir işlem kullanarak birden fazla ölçeğe ayırmak ve ardından EADA yöntemiyle her ölçeğin ölçeklenme davranışını tahmin etmektir. Bu, zaman serilerinin çok fraktal özelliklerini tanımlayan bir dizi ölçeklendirme üssü verir. ÇF-EADA sonuçlarımız, tüm S&P 500 sektör endekslerinde çoklu fraktalitenin varlığını göstermektedir. Bu indeksler çoklu fraktal olduğundan, ölçekleme değişkenliği, doğrusal olmayan dinamikler, kendine benzerlik, uzun menzilli bağımlılık, çok ölçekli korelasyonlar ve durağan olmama gibi özelliklere sahip oldukları sonucuna varabiliriz.

Keywords

• Multifraktalite
• MF-TADA
• Multifraktal Trendden Arındırılmış Dalgalanma Analizi
• Fraktal Teori
• S&P 500

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