Robust q-negative Multifractal Detrended Cross-Correlation Coefficient
Abstract
The multifractal detrended cross-correlation coefficient ρq(n) is widely used to investigate scale-dependent interactions, but its application to negative fluctuation orders is affected by numerical instabilities, unbounded values, and interpretational difficulties. We propose a Signed Multifractal Detrended Cross-Correlation Coefficient, ρSMFDCCA(n,q), an amplitude-conditioned correlation observable for multifractal detrended analysis, based on locally normalized detrended correlations and regularized fluctuation amplitudes. The proposed coefficient preserves the sign of local interactions, remains strictly bounded within [−1,1] for both positive and negative values of q, and eliminates the corrective procedures required by previous approaches. Validation using independent fractional Gaussian noise confirms the absence of spurious cross-correlations and the numerical stability of the method. Applications demonstrate that the proposed observable resolves how cross-correlations evolve jointly with temporal scale and fluctuation amplitude, revealing scale- and amplitude-dependent correlation structures, including stronger synchronization during large fluctuations in stock-market indices and heterogeneous coupling patterns in temperature records.
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BibTeX
@misc{murari2026robust,
title = {{Robust q-negative Multifractal Detrended Cross-Correlation Coefficient}},
author = {Thiago B. Murari and José Fernando F. Mendes and Hernane B. B. Pereira and Marcelo A. Moret},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.06324},
eprint = {2607.06324},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.06324},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Robust q-negative Multifractal Detrended Cross-Correlation Coefficient
AU - Thiago B. Murari
AU - José Fernando F. Mendes
AU - Hernane B. B. Pereira
AU - Marcelo A. Moret
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2607.06324
UR - https://arxiv.org/abs/2607.06324
AB - The multifractal detrended cross-correlation coefficient ρ_q(n) is widely used to investigate scale-dependent interactions, but its application to negative fluctuation orders is affected by numerical instabilities, unbounded values, and interpretational difficulties. We propose a Signed Multifractal Detrended Cross-Correlation Coefficient, ρ_SMFDCCA(n,q), an amplitude-conditioned correlation observable for multifractal detrended analysis, based on locally normalized detrended correlations and regularized fluctuation amplitudes. The proposed coefficient preserves the sign of local interactions, remains strictly bounded within [−1,1] for both positive and negative values of q, and eliminates the corrective procedures required by previous approaches. Validation using independent fractional Gaussian noise confirms the absence of spurious cross-correlations and the numerical stability of the method. Applications demonstrate that the proposed observable resolves how cross-correlations evolve jointly with temporal scale and fluctuation amplitude, revealing scale- and amplitude-dependent correlation structures, including stronger synchronization during large fluctuations in stock-market indices and heterogeneous coupling patterns in temperature records.
ER -