The paper introduces new methods to measure cross-correlations between time series using power-law coherency.
problem Studying power-law cross-correlations between time series.
method Three estimators of the power-law coherency parameter H_ρ based on DCCA, DMCA, and HXA.
result DMCA-based method is the safest choice, HXA method is reasonable for long series, and DCCA-based method has unfavorable properties.
The study finds significant power-law cross correlations in Bitcoin's return-volatility dynamics.
problem Investigating asymmetry in Bitcoin's return-volatility relationships.
method Analysis of daily and high-frequency Bitcoin data to identify cross correlations.
result Power-law cross correlations between returns and future volatilities are observed, indicating long-range dependencies.
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 Hurst exponent is then equa…
We introduce a new test for detection of power-law cross-correlations among a pair of time series - the rescaled covariance test. The test is based on a power-law divergence of the covariance of the partial sums of the long-range cross-correlated processes. Utilizing a heteroskedasticity and auto-correlation robust est…
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 power-law coherency. Presen…
New method detects intrinsic cross-correlations in non-stationary time series affected by common factors.
problem Bias in cross-correlation analysis due to common external factors.
method Multifractal temporally weighted detrended partial cross-correlation analysis (MF-TWDPCCA).
result MF-TWDPCCA accurately detects intrinsic cross-correlations between non-stationary time series.
Study examines power-law cross-correlations under heavy-tailed distributions.
problem Estimating power-law cross-correlations under heavy-tailed distributions.
method Examined six estimators: detrended cross-correlation, detrending moving-average, height cross-correlation, averaged periodogram, cross-periodogram, local cross-Whittle.
result Time domain estimators are biased for heavy tails but have lower variance than frequency domain estimators.
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 are at the same time lo…
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 show that the searche…
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 from physics, physiology,…
It is ubiquitous in natural and social sciences that two variables, recorded temporally or spatially in a complex system, are cross-correlated and possess multifractal features. We propose a new method called multifractal detrended cross-correlation analysis (MF-DXA) to investigate the multifractal behaviors in the pow…
We consider a few quantities that characterize trading on a stock market in a fixed time interval: logarithmic returns, volatility, trading activity (i.e., the number of transactions), and volume traded. We search for the power-law cross-correlations among these quantities aggregated over different time units from 1 mi…
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 analysis (DPXA) to uncover…
Study on oil price's multifractal cross-correlations with other financial markets.
problem Analyzing statistical and multiscaling characteristics of oil prices and their cross-correlations with other financial instruments.
method Multifractal analysis, detrended cross-correlation coefficient, multifractal cross-correlation analysis.
result Multifractal cross-correlations between oil prices and other financial markets, especially with oil-producing countries' currencies.
We consider the effects of the global financial crisis through a local Korean financial market around the 2008 crisis. We analyze 185 individual stock prices belonging to the KOSPI (Korea Composite Stock Price Index), cosidering three time periods: the time before, during, and after the crisis. The complex networks gen…
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 quantify risk, and find that …
Econophysics explores power-law correlations in financial markets.
problem Analyzing long-range dependencies and power-law correlations in financial data.
method Generalization of methods from outside finance to financial time series, focusing on bivariate settings.
result Rapid development in econophysics has revealed new challenges and issues.
There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. The multifractal detrended cross-correlation analysis (MF-DCCA) approaches can be used to quantify such cross-correlations, such as the MF-DCCA based on detrend…
Analyzes financial return distributions over various time scales.
problem Understanding the changing nature of financial return distributions over time.
method Modeling return distributions using power-law, stretched exponential, and q-Gaussian functions.
result The 'inverse-cubic power-law' is still a good fit for short-term returns, but market dynamics are more complex.
In finance, one usually deals not with prices but with growth rates R, defined as the difference in logarithm between two consecutive prices. Here we consider not the trading volume, but rather the volume growth rate R~, the difference in logarithm between two consecutive values of trading volume. To this end…
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 Hxy<12(Hx+Hy) but also for long-range …
We study a stochastic multiplicative system composed of finite asynchronous elements to describe the wealth evolution in financial markets. We find that the wealth fluctuations or returns of this system can be described by a walk with correlated step sizes obeying truncated Levy-like distribution, and the cross-correla…
We investigate the two components of the total daily return (close-to-close), the overnight return (close-to-open) and the daytime return (open-to-close), as well as the corresponding volatilities of the 2215 NYSE stocks from 1988 to 2007. The tail distribution of the volatility, the long-term memory in the sequence, a…
Study on price-volume correlation fractal features and market type effects.
problem Understanding the fractal features and market type effects of price-volume correlation.
method Applied MF-DXA method to analyze price, trading volume, and their coupling.
result Price, trading volume, and price-volume coupling exhibit power law and multifractal properties.
We introduce two new estimators of the bivariate Hurst exponent in the power-law cross-correlations setting -- the cross-periodogram and local X-Whittle estimators -- as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration …
We study the cross-correlation matrix Cij of inventory variations of the most active individual and institutional investors in an emerging market to understand the dynamics of inventory variations. We find that the distribution of cross-correlation coefficient Cij has a power-law form in the bulk followed by …
The paper proposes new cross-correlators using Price's Theorem and piecewise-linear decomposition.
problem Optimal method for estimating cross-correlations using finite samples.
method General mathematical framework using Price's Theorem and piecewise-linear decomposition.
result Some cross-correlators based on Huber's loss functions, MP functions, and LSE functions have higher SNR.
Cryptocurrency market becomes more cross-correlated over time.
problem Understanding the inter-market dependencies of cryptocurrencies.
method Time series analysis, spectral analysis, topological analysis of minimal spanning trees.
result Cryptocurrency market becomes more cross-correlated with other markets over time.
We introduce a new method for detection of long-range cross-correlations and multifractality - multifractal height cross-correlation analysis (MF-HXA) - based on scaling of qth order covariances. MF-HXA is a bivariate generalization of the height-height correlation analysis of Barabasi & Vicsek [Barabasi, A.L., Vicsek,…
We propose a novel algorithm - Multifractal Cross-Correlation Analysis (MFCCA) - that constitutes a consistent extension of the Detrended Cross-Correlation Analysis (DCCA) and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for …
A new method detects long-range cross correlations in complex systems.
problem Detecting long-range cross correlations in complex systems.
method Joint multifractal analysis based on wavelet leaders (MF-X-WL).
result MF-X-WL detects cross correlations in synthetic and real-world data.
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only o…
Study uses multifractal detrended cross-correlation to detect Forex arbitrage opportunities.
problem Detecting arbitrage opportunities in Forex markets.
method Multifractal detrended cross-correlation analysis applied to Forex time series.
result Strong cross-correlations found between exchange rates involved in triangular relations, including AUD and NZD.
Study finds multifractal cross-correlations between agricultural markets and external uncertainties.
problem Investigating relationships between agricultural spot markets and external uncertainties.
method Multifractal detrending moving-average cross-correlation analysis (MF-X-DMA).
result Maize exhibits intrinsic joint multifractality with all uncertainty proxies.
Study on cryptocurrency trading patterns using multifractal analysis.
problem Lack of systematic study on temporal structure of cryptocurrency trading.
method Multifractal detrended cross-correlation analysis of price returns, trades, and volume.
result All analyzed quantities exhibit multifractal structure, both univariate and bivariate.
Study stock market instability using cross-correlation matrices and principal components analysis.
problem Quantifying and analyzing volatility in the Tokyo Stock Exchange.
method Rolling window cross-correlation matrices, principal components analysis, and random matrix theory.
result Detected three volatile market stages: Lehman Brothers bankruptcy, Tohoku Earthquake, and QE3 reduction.
We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be positively correlated to their depth in the hierarchy of cross-correlations. We propose…
Study uses detrended cross-correlation to analyze cryptocurrency market, revealing robust collective modes and distinguishing interdependencies.
problem Nonstationarity, long-range memory, and heavy-tailed fluctuations obscure traditional correlations in complex systems.
method Constructs detrended correlation matrices using multifractal detrended cross-correlation coefficient ρr to emphasize different fluctuations. result Detrending and fluctuation analysis reveal distinct spectral properties from random case, identifying market and sectoral components.
Paper models dynamic multivariate functional data with sparse subspace learning.
problem Complex, high-dimensional multivariate functional data with evolving cross-correlations.
method Sparse subspace learning for automatic subspaces formulation and cross-correlation dynamics description.
result Efficient estimation and feature extraction of multivariate functional data.
A new method for analyzing multifractal cross correlations in complex systems.
problem Characterizing long-range cross-correlations in complex systems.
method Multifractal Cross Wavelet Analysis (MFXWT)
result MFXWT accurately captures joint multifractality in binomial multifractal measures but may produce spurious results for bivariate fractional Brownian motions.
We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the correlation matrix is positively…
In order to pursue the issue of the relation between the financial cross-correlations and the conventional Random Matrix Theory we analyse several characteristics of the stock market correlation matrices like the distribution of eigenvalues, the cross-correlations among signs of the returns, the volatility cross-correl…
This study examines asymmetric cross-correlations in cryptocurrency markets using fractal analysis.
problem Exploring asymmetric multifractal cross-correlations in cryptocurrency markets.
method Fractal analysis and MF-ADCCA method to investigate asymmetric volatility dynamics.
result Cross-correlations are stronger in downtrend markets than in uptrend markets for maturing BTC and ETH.
An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average instantaneous cross-correlations is investigated over different price return time inte…
Clusters cryptocurrency market states via cross correlation analysis.
problem Analyse cryptocurrency market dynamics.
method Cross correlation structure analysis over 5 years.
result Cryptocurrency market clusters into 4 states.
New methods improve cross-correlation analysis of time series data.
problem Controversies in Multifractal detrended cross-correlation analysis.
method Proposes new options to handle negative cross-covariance.
result Improved robustness in multifractal spectrum analysis.
Novel beamforming method reduces errors in wireless networks.
problem Mitigating channel errors in wireless networks with relays.
method Low-rank and cross-correlation techniques for robust distributed beamforming.
result The proposed LRCC-RDB technique significantly improves SINR performance.
We analyse the temporal changes in the cross correlations of returns on the New York Stock Exchange. We show that lead-lag relationships between daily returns of stocks vanished in less than twenty years. We have found that even for high frequency data the asymmetry of time dependent cross-correlation functions has a d…