We use a new method of studying the Hurst exponent with time and scale dependency. This new approach allows us to recover the major events affecting worldwide markets (such as the September 11th terrorist attack) and analyze the way those effects propagate through the different scales. The...

The WIG20 index–the index of the 20 biggest companies traded on the Warsaw Stock Exchange–reached the global maximum on 29th October 2007. I have used the local DFA (Detrended Functional Analysis) to obtain the Hurst exponent (diffusion exponent) and investigate the signature of...

We report an empirical study of the Ibovespa index of the São Paulo Stock Exchange in which we detect the existence of long-range correlations. To analyze our data, we introduce a rescaled variant of the usual detrended fluctuation analysis that allows us to obtain the Hurst exponent through a...

The Euro (EUR) is a new currency introduced by the European Community. Its exchange rate is very puzzling. We have invented a false Euro (FEUR) dating back to 1993 and have derived the exchange rates of the FEUR with respect to currencies not belonging to the EUR, i.e., DKK,CHF,JPY and USD. This...

In our work copula functions and the Hurst exponent calculated using the local Detrended Fluctuation Analysis (DFA) were used to investigate the risk of investment made in shares traded on the Warsaw Stock Exchange. The combination of copula functions and the Hurst exponent calculated using...

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...

In this paper the two dimensional model of the investment in shares is presented. The shares prices from five different world stock exchanges (New York, London, Frankfurt, Honk Kong, and Sydney) are examined. The copula functions are used to model the risk of investment. The Hurst threshold...

We report an empirical study of Tehran price index (TEPIX). To analyze our data we use various methods like as, rescaled range analysis (R/S), modified rescaled range analysis (Lo's method), detrended fluctuation analysis (DFA) and generalized Hurst exponents analysis. Based on numerical...

The length of minimal and maximal blocks equally distant on log–log scale versus fluctuation function considerably influences bias and variance of DFA. Through a number of extensive Monte Carlo simulations and different fractional Brownian motion/fractional Gaussian noise generators, we found...

A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long-range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of different lengths. We...