Multifractal Detrended Cross-Correlation Analysis of Sunspot Numbers and River Flow Fluctuations. Hajian, S. & Movahed, M. S. 389(21):4942–4957.
Multifractal Detrended Cross-Correlation Analysis of Sunspot Numbers and River Flow Fluctuations [link]Paper  doi  abstract   bibtex   
We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, (12-24) ≤ s ≤ 130 months, is λ =1.17±0.04 which is almost similar for all underlying rivers at 1 σ confidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long range cross-correlation between the sunspot numbers and underlying streamflow records. The magnitude of the scaling exponent and corresponding cross-correlation exponent are λ (0.76,0.85) and γ × (0.30,0.48) , respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), inlMMLBox is confirmed.
@article{hajianMultifractalDetrendedCrossCorrelation2010,
  title = {Multifractal {{Detrended Cross}}-{{Correlation Analysis}} of Sunspot Numbers and River Flow Fluctuations},
  author = {Hajian, S. and Movahed, M. Sadegh},
  date = {2010-11},
  journaltitle = {Physica A: Statistical Mechanics and its Applications},
  volume = {389},
  pages = {4942--4957},
  issn = {0378-4371},
  doi = {10.1016/j.physa.2010.06.025},
  url = {https://doi.org/10.1016/j.physa.2010.06.025},
  abstract = {We use the Detrended Cross-Correlation Analysis (DCCA) to investigate the influence of sun activity represented by sunspot numbers on one of the climate indicators, specifically rivers, represented by river flow fluctuation for Daugava, Holston, Nolichucky and French Broad rivers. The multifractal Detrended Cross-Correlation Analysis (MF-DXA) shows that there exist some crossovers in the cross-correlation fluctuation function versus time scale of the river flow and sunspot series. One of these crossovers corresponds to the well-known cycle of solar activity demonstrating a universal property of mentioned rivers. The scaling exponent given by DCCA for original series at intermediate time scale, (12-24) ≤ s ≤ 130 months, is λ =1.17±0.04 which is almost similar for all underlying rivers at 1 σ confidence interval showing the second universal behavior of river runoffs. To remove the sinusoidal trends embedded in data sets, we apply the Singular Value Decomposition (SVD) method. Our results show that there exists a long range cross-correlation between the sunspot numbers and underlying streamflow records. The magnitude of the scaling exponent and corresponding cross-correlation exponent are λ (0.76,0.85) and γ × (0.30,0.48) , respectively. Different values for scaling and cross-correlation exponents may be related to local and external factors such as topography, drainage network morphology, human activity and so on. Multifractal cross-correlation analysis demonstrates that all underlying fluctuations have almost weak multifractal nature which is also a universal property for data series. In addition the empirical relation between scaling exponent derived by DCCA and Detrended Fluctuation Analysis (DFA), inlMMLBox is confirmed.},
  keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-7382105,climate-change,correlation-analysis,cyclostationarity,fractal,nonlinear-correlation,river-flow,solar-energy,water-resources},
  number = {21}
}
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