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,...

By testing 88 different funds of the Chinese fund market (CFM), we find fractal behavior and long-range correlations in the return series, which are insensitive to the kind of funds. Meanwhile, a power-law relationship between the deviation D of prices and the Hurst exponent H has been obtained,...

It is discussed by the use of simulations how the self-similar nature emerges in the computer network traffic. We propose a new model which incorporates the realistic communication procedure. In this model, the self-similarity is partially realized depending on the maximum data length and not on...

The influence of the1998 Russian financial crisis on the statistical properties of currencies in transition economies has been studied. Essential changes before and after crisis were discovered. All effects are essentially nonlinear and differ from the ones in advanced economies.

Zonation of time series into models which their parameters are piecewise constant are important and well-studied problems. Geophysical well logging data often show a complex pattern due to their multifractal nature. In a multifractal system, any pieces of it are established by a distinct...

Processes with long-range dependence (LRD) have gained wide applications in many fields of science and technologies ranging from hydrology to network traffic. Two key properties of such processes are LRD that is characterized by the Hurst parameter H and self-similarity (SS) that is measured by...

Fracture induced physical fields allow a real-time monitoring of damage evolution in materials during mechanical loading. We investigate the preparation of the recently occurred L’Aquila earthquake in terms of a detected precursory electromagnetic anomaly. The precursor is well described by a...