In this note, we investigate possible relationships between the bivariate Hurst exponent Hxy and an average of the separate Hurst exponents 12(Hx+Hy). We show that two cases are well theoretically founded. These are the cases when Hxy=12(Hx+Hy) and Hxy<12(Hx+Hy). However, we show that the case of Hxy>12(Hx+Hy) is not possible regardless of...</12(hx+hy).>

We study finite sample properties of estimators of power-law cross-correlations–detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA)–with a special focus on short-term memory bias as well as...

We inspect a possible clustering structure of the corruption perception among 134 countries. Using the average linkage clustering, we uncover a well-defined hierarchy in the relationships among countries. Four main clusters are identified and they suggest that countries worldwide can be quite...

We study power-law correlations properties of the Google search queries for Dow Jones Industrial Average (DJIA) component stocks. Examining the daily data of the searched terms with a combination of the rescaled range and rescaled variance tests together with the detrended fluctuation analysis,...

We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate...

In the paper, we introduce a new measure of correlation between possibly non-stationary series. As the measure is based on the detrending moving-average cross-correlation analysis (DMCA), we label it as the DMCA coefficient ρDMCA(λ) with a moving average window length λ. We analytically show...

In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlation detection — classical and modified rescaled range analyses. A focus is put on an effect of different distributional properties on an ability of the methods to efficiently...

In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF-DFA), detrending moving...

We introduce a new measure for capital market efficiency. The measure takes into consideration the correlation structure of the returns (long-term and short-term memory) and local herding behavior (fractal dimension). The efficiency measure is taken as a distance from an ideal efficient market...

We introduce a general framework of the Mixed-correlated ARFIMA (MC-ARFIMA) processes which allows for various specifications of univariate and bivariate long-term memory. Apart from a standard case when Hxy=12(Hx+Hy), MC-ARFIMA also allows for processes with Hxy12(Hx+Hy) but also for long-range...