We apply the Hurst exponent idea for investigation of DJIA index time-series data. The behavior of the local Hurst exponent prior to drastic changes in financial series signal is analyzed. The optimal length of the time-window over which this exponent can be calculated in order to make some...

We investigate the local fractal properties of the financial time series based on the whole history evolution (1991–2007) of the Warsaw Stock Exchange Index (WIG), connected with the largest developing financial market in Europe. Calculating the so-called local time-dependent Hurst exponent...

The Zipf analysis of n-words in random sequences and financial data series like the stock prices of a company has been performed. The bias as well as the resulting staircase structure of the Zipf plots are taken into account in the subsequent analysis. It is found that correlations for the sign...

We analyze proportional election data to show the influence of parties on the results of this kind of election. The study compiles data from different countries and dates to show that depending on how the candidate’s votes are counted, one can find that these votes have different...

We examine the scaling regime for the detrended fluctuation analysis (DFA)—the most popular method used to detect the presence of long-term memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of time series...

Axial Graphs are networks whose nodes are linear axes in urban space, and whose edges represent intersections of such axes. These graphs are used in urban planning and urban morphology studies. In this paper we analyse distance distributions between nodes in axial graphs, and show that these...

Analytical arguments are used to describe the behavior of the average velocity in the problem of an ensemble of particles bouncing a heavy and periodically moving platform. The dynamics of the system is described by using a two-dimensional mapping for the variables’ velocity and discrete time...

This paper presents the multifractal model of asset returns ("MMAR"), based upon the pioneering research into multifractal measures by Mandelbrot (1972, 1974). The multifractal model incorporates two elements of Mandelbrot's past research that are now well-known in finance. First, the MMAR...

This paper presents the first empirical investigation of the Multifractal Model of Asset Returns ("MMAR"). The MMAR, developed in Mandelbrot, Fisher, and Calvet (1997), is an alternative to ARCH-type representations for modelling temporal heterogeneity in financial returns. Typically,...