Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations

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 the 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 1σconfidence 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 the underlying streamflow records. The magnitude of the scaling exponent and the 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), λ ≈ (hsun + hriver)/2 is confirmed.

The Time-Scaling Analysis of Chinese Stock Market Based on Fractal Methods

“…Multifractal analysis has been applied to several fields of the scientific research. The related literatures can be seen in the further detail computation [6].…”

Multifractal Detrended Fluctuation Analysis of Streamflow in the Yellow River Basin, China

“…Hurst's finding is recognized as the first example of self-affine fractal behavior in empirical time series [6]. Since then, many researchers have shown great interest in detecting the long-range correlation of streamflow [7][8][9][10][11][12]. In these studies, detrended fluctuation analysis (DFA) was commonly applied to investigate the long-range correlation of streamflow.…”

Coupled uncertainty provided by a multifractal random walker

“…Multifractal models have been implemented in various fields of sciences ranging from biology, geology, social to finance, e.g. Earth & Solar winds [20][21][22], foreign exchange rates [23], stock index [24,25], human heartbeat fluctuations [26,27], welllog data [28] seismic time series [29][30][31][32], and sol-gel transitions [33][34][35].…”