Financial markets exhibit a complex hierarchy among different processes, e.g. a trading time marks the initiation of a trade, and a trade triggers a price change. High-frequency trading data arrive at random times. By combining stochastic and agent-based approaches, we develop a model for...

We propose a modified time lag random matrix theory in order to study time lag cross-correlations in multiple time series. We apply the method to 48 world indices, one for each of 48 different countries. We find long-range power-law cross-correlations in the absolute values of returns that...

When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using classic detrended cross-correlation analysis (DCCA) without considering these common factors will bias the results. We use detrended partial cross-correlation...

Housing markets play a crucial role in economies and the collapse of a real-estate bubble usually destabilizes the financial system and causes economic recessions. We investigate the systemic risk and spatiotemporal dynamics of the US housing market (1975-2011) at the state level based on the...

We report quantitative relations between corruption level and economic factors, such as country wealth and foreign investment per capita, which are characterized by a power law spanning multiple scales of wealth and investments per capita. These relations hold for diverse countries, and also...

We investigate how simultaneously recorded long-range power-law correlated multi-variate signals cross-correlate. To this end we introduce a two-component ARFIMA stochastic process and a two-component FIARCH process to generate coupled fractal signals with long-range power-law correlations which...

In order to investigate whether government regulations against corruption can affect the economic growth of a country, we analyze the dependence between Gross Domestic Product (GDP) per capita growth rates and changes in the Corruption Perceptions Index (CPI). For the period 1999-2004 on average...

Here we propose a method, based on detrended covariance which we call detrended cross-correlation analysis (DXA), to investigate power-law cross-correlations between different simultaneously-recorded time series in the presence of non-stationarity. We illustrate the method by selected examples...

We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy distribution. For both (i) and (ii), we find that due to the...

We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy stability for the probability density, and hence shows scaling properties (as observed in empirical data); it has the...