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This paper introduces a multiscale multifractal multiproperty analysis based on Rényi entropy (3MPAR) method to analyze short-range and long-range characteristics of financial time series, and then applies this method to the five time series of five properties in four stock indices. Combining the two analysis techniques of Rényi entropy and multifractal detrended fluctuation analysis (MFDFA), the 3MPAR method focuses on the curves of Rényi entropy and generalized Hurst exponent of five properties of four stock time series, which allows us to study more universal and subtle fluctuation characteristics of financial time series. By analyzing the curves of the Rényi entropy and the profiles of the logarithm distribution of MFDFA of five properties of four stock indices, the 3MPAR method shows some fluctuation characteristics of the financial time series and the stock markets. Then, it also shows a richer information of the financial time series by comparing the profile of five properties of four stock indices. In this paper, we not only focus on the multifractality of time series but also the fluctuation characteristics of the financial time series and subtle differences in the time series of different properties. We find that financial time series is far more complex than reported in some research works using one property of time series.

For the purpose of transmitting data in smart grids, broadband communication over power lines (PLC) is considered to be one of the feasible technologies. Due to the multi-path effect of the signal propagation in complicate electrical networks, PLC signals present some dynamic features in time and space domains. The mono-fractal and multi-fractal theories are introduced to understand such dynamic features in PLC signals. Four common methods, namely, re-scaled range analysis, variance–time plot method, periodic diagram analysis and wavelet-based method are used to study the nonlinear properties and self-similarity. Fractal analysis at different frequencies and times is also performed to verify further. The paper also tests multi-fractal properties of PLC signals by the means of multi-fractal detrended fluctuation analysis (MFDFA). The multi-fractal spectrum of power low exponents is estimated from the measured PLC signals. We also proposed a new algorithm to improve the performance of the traditional MFDFA, where wavelet theory is integrated. By simulations, the better performance of the proposed method is verified.

Based on high-frequency data, we study the difference in cryptocurrency market before and during the COVID-19. We analyze the multifractality of three major cryptocurrencies via the multifractal detrended fluctuation analysis (MFDFA). To investigate the source of multifractality, we construct shuffled, surrogated and truncate data. The results show that market efficiency of cryptocurrency has decreased during COVID-19. The cryptocurrency multifractal characteristics mainly come from non-Gaussian distribution. Additionally, the components of multifractal nature have changed during the pandemic. The results provide evidence for the impact of COVID-19 on cryptocurrency market.

This study evaluates the Brazilian agricultural commodities market and the dollar–real exchange price variation using the multifractal detrended fluctuations analysis methodology. We investigated the period from January 1, 2019 to September 25, 2019, outside the COVID-19 pandemic, and from January 1, 2020 to September 25, 2020, during the COVID-19 pandemic. We verified the fluctuations of commodities and dollar–real exchange prices during the pandemic caused by COVID-19 showed a record price. The results of Hurst exponent and multifractal parameters ${\alpha }_0$, $w$, and $r$ indicate that during the COVID-19 pandemic, sugar was the most efficient commodity, while pork the less one. Compared to the identical months in 2019, the dollar–real exchange was the most efficient market, while ethanol was the least efficient.

Over the years, the (multi)fractal nature of signals describing the activity of ion channels has been observed both at the level of single-channel currents and the temporal scaling of the corresponding sojourns in conducting and non-conducting states. The recognized nonlinear and self-similar properties were interpreted regarding the underlying channel gating machinery. Nevertheless, the literature lacks in (multi)fractal description of the biochemical stimulation of ion channels. Therefore, in this work, we provide a multifractal description of the effects exerted by two different flavonoids — naringenin (Nar) and quercetin (Que) — being the regulators of the large-conductance voltage- and Ca${}^{2+}$-activated K${}^{+}$ channels from the inner mitochondrial membrane (mitoBK). Toward this aim, the focus-based multifractal detrended fluctuation analysis (MFDFA) was applied to the patch-clamp data obtained in the presence of Nar and Que in micromolar concentrations and the corresponding controls. Our results show that mitoBK channel activity has well-pronounced multifractal characteristics and long-range memory (measured by the generalized Hurst exponent) under biochemical stimulation by Nar and Que and in the absence of these substances. The spectral properties significantly change after the randomization of the analyzed series. Therefore, multifractality is an inherent feature of the mitoBK channel currents, which stems from their statistical distribution and temporal organization. Both flavonoids have similar structures and exert channel-activating effects, but they differently affect the parameters of the multifractal spectra of the corresponding patch-clamp signals. Coordination of Que leads to more prominent changes in signal complexity than Nar at membrane hyper- and depolarization. It suggests that this flavonoid has a stronger impact on the conformational dynamics of the mitoBK channels in comparison with naringenin.

This work involves the application of a non-linear method, multifractal detrended fluctuation analysis (MFDFA), to describe fish sound data recorded from the open waters of two major estuarine systems. Applying MFDFA, the second-order Hurst exponent $h(q=2)$ values are found to be $1.10\pm 0.03$ and $1.43\pm 0.02$ for the fish families Batrachoididae (common name: Toadfish) and Sciaenidae (common name: Croakers, drums), respectively. The generalized Hurst exponent $h(q)$-related width parameters $\mathrm{\Delta }h(q)$ are found to be $1.05\pm 0.08$ and $0.94\pm 0.06$, respectively, for toadfish and Sciaenidae vocalizations, implying greater heterogeneity and multifractal characteristics. The results suggest that the Sciaenidae fish calls are smoother in comparison with Batrachoididae. Clustering of multifractal spectrum-related parameters with respect to toadfish and Sciaenidae vocalization characteristics is observed in this analyses.

Tropical countries, like Nigeria, depend on rainfall for agriculture, power generation, transportation and other economic activities. Drought will hinder the performance of these activities, hence, it poses a significant threat to the economy. Understanding fluctuations and structures in droughts will help in forecasting, planning and mitigating its impact on livelihoods. In this study, the multifractal properties of drought at four temporal scales were investigated over different locations across Nigeria. Drought was computed using the standardized precipitation index from monthly precipitation data from 1980 to 2010. Using multifractal detrended fluctuation analysis, meteorological drought was found to have multifractal properties at 1-, 6-, 12- and 24-month temporal scale. The generalized Hurst exponent of drought at different time-scale showed dependence on scaling exponent. Long-range correlations were found to be main source of multifractality at all temporal scales. The multifractal strength increases with increasing temporal scale except for a few locations. The range of spectrum width were found to be 0.306–0.464 and 0.596–0.993 at 1- and 24-month temporal scale, respectively. No significant trend was found in the degree of multifractality across different climatic zones of Nigeria.