DCCA cross-correlation coefficient differentiation: Theoretical and practical approaches

Zebende, Gilney Figueira; Silva, M.F. da; Filho, A. Machado

doi:10.1016/j.physa.2013.01.011

Cited by 100 publications

(54 citation statements)

References 26 publications

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“…Based on both methods, the socalled detrended cross-correlation coefficient ρ DCCA was introduced that is a counterpart of the Pearson correlation coefficient [37]. It can be used in the case of nonstationary data to quantify strength of cross-correlations between detrended signals at a given time scale [37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations

et al. 2017

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Based on a recently proposed q-dependent detrended cross-correlation coefficient, ρ_{q} [J. Kwapień, P. Oświęcimka, and S. Drożdż, Phys. Rev. E 92, 052815 (2015)PLEEE81539-375510.1103/PhysRevE.92.052815], we generalize the concept of the minimum spanning tree (MST) by introducing a family of q-dependent minimum spanning trees (qMSTs) that are selective to cross-correlations between different fluctuation amplitudes and different time scales of multivariate data. They inherit this ability directly from the coefficients ρ_{q}, which are processed here to construct a distance matrix being the input to the MST-constructing Kruskal's algorithm. The conventional MST with detrending corresponds in this context to q=2. In order to illustrate their performance, we apply the qMSTs to sample empirical data from the American stock market and discuss the results. We show that the qMST graphs can complement ρ_{q} in disentangling "hidden" correlations that cannot be observed in the MST graphs based on ρ_{DCCA}, and therefore, they can be useful in many areas where the multivariate cross-correlations are of interest. As an example, we apply this method to empirical data from the stock market and show that by constructing the qMSTs for a spectrum of q values we obtain more information about the correlation structure of the data than by using q=2 only. More specifically, we show that two sets of signals that differ from each other statistically can give comparable trees for q=2, while only by using the trees for q≠2 do we become able to distinguish between these sets. We also show that a family of qMSTs for a range of q expresses the diversity of correlations in a manner resembling the multifractal analysis, where one computes a spectrum of the generalized fractal dimensions, the generalized Hurst exponents, or the multifractal singularity spectra: the more diverse the correlations are, the more variable the tree topology is for different q's. As regards the correlation structure of the stock market, our analysis exhibits that the stocks belonging to the same or similar industrial sectors are correlated via the fluctuations of moderate amplitudes, while the largest fluctuations often happen to synchronize in those stocks that do not necessarily belong to the same industry.

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Section: Introductionmentioning

confidence: 99%

Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations

et al. 2017

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“…For the two returns {r i (t)} and {r j (t)} of currencies i and j, the DCCA coefficient is defined as the ratio between the detrended covariance function F 2 DCCA (s) of Equation (4) and two detrended variance functions F DFA (s) of Equation (5) [48,50,51,53], i.e.,…”

Section: Methodsmentioning

confidence: 99%

“…An outstanding advantage of the DCCA coefficient (another expression of ρ i j (s)) is that it can examine the cross-correlations between non-stationary time series at different time scales [4,45]. After that, the DCCA coefficient was widely used to investigate the cross-correlations in different fields [50,51], such as the FX market [4,52] and stock markets [45,53,54].…”

Section: Introductionmentioning

confidence: 99%

Statistical Properties of the Foreign Exchange Network at Different Time Scales: Evidence from Detrended Cross-Correlation Coefficient and Minimum Spanning Tree

Wang

Xie

Chen

et al. 2013

Entropy

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Abstract:We investigate the statistical properties of the foreign exchange (FX) network at different time scales by two approaches, namely the methods of detrended cross-correlation coefficient (DCCA coefficient) and minimum spanning tree (MST). The daily FX rates of 44 major currencies in the period of 2007-2012 are chosen as the empirical data. Based on the analysis of statistical properties of cross-correlation coefficients, we find that the cross-correlation coefficients of the FX market are fat-tailed. By examining three MSTs at three special time scales (i.e., the minimum, medium, and maximum scales), we come to some conclusions: USD and EUR are confirmed as the predominant world currencies; the Middle East cluster is very stable while the Asian cluster and the Latin America cluster are not stable in the MSTs; the Commonwealth cluster is also found in the MSTs. By studying four evaluation criteria, we find that the MSTs of the FX market present diverse topological and statistical properties at different time scales. The scale-free behavior is observed in the FX network at most of time scales. We also find that most of links in the FX network survive from one time scale to the next.

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“…Taking into account that has been said above, in this paper we analyze the cross-correlation between Ibovespa and the blue-chips from a well-defined relationship between α DFA and λ DCCA exponents [21]. Thus, in the following section we present briefly this theory in the sense of improving this paper.…”

Section: The ρ Dcca Coefficient [2]mentioning

confidence: 97%

Quantifying cross-correlation between Ibovespa and Brazilian blue-chips: The DCCA approach

Silva

Pereira

Filho

et al. 2015

Physica A: Statistical Mechanics and its Applications

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DCCA cross-correlation coefficient differentiation: Theoretical and practical approaches

Cited by 100 publications

References 26 publications

Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations

Minimum spanning tree filtering of correlations for varying time scales and size of fluctuations

Statistical Properties of the Foreign Exchange Network at Different Time Scales: Evidence from Detrended Cross-Correlation Coefficient and Minimum Spanning Tree

Quantifying cross-correlation between Ibovespa and Brazilian blue-chips: The DCCA approach

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