Analysis on historical data of stock indices using Fractal dimension methods by measuring the complexity

Abstract

Fractal dimension is a nonlinear fractal concept, which is used for analyzing the complexity of stock indices. In this paper we execute fractal dimension (FD) concept for analyzing the complexity of stock indices. From different sectors, the closing price indices of stock indices BSESN, NYSE, NSE-Nifty and NASDAQ are chosen for the investigation and the outcome on research are exhibited on that wide-open convenient dataset associated with various kinds of stock indices data. Four notable assessment methods, namely Generalized fractal dimension (GFD), Katz's Fractal dimension (KFD), Higuchi's Fractal dimension (HFD) and Sevcik's Fractal dimension (SFD) methods are examined in this investigation for the classification of complex stock data. The whole stock indices data is separated into subgroups with different sizing for the computation of fractal dimension which leads this research to the multifractal analysis. Anlaysis data set through subgroups with different size exhibits multifractal behavior. The whole data considered represents random walk for all the stock indices. The regarded exchange data of the indices are irregular and randomized in nature and authorize to employ fractal analysis. The results show that KFD method is more consistent than the results obtained by GFD, HFD and SFD methods.