Multifractal Properties of Meteorological Drought at Different Time Scales in a Tropical Location

2020 ◽  
pp. 2150007
Author(s):  
Samuel Toluwalope Ogunjo
Keyword(s):  
Standardized Precipitation Index ◽  
Meteorological Drought ◽  
Temporal Scale ◽  
Fluctuation Analysis ◽  
Monthly Precipitation ◽  
Scaling Exponent ◽  
Economic Activities ◽  
Temporal Scales ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Long Range Correlations

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.

FLUCTUATION BEHAVIOR OF FINANCIAL RETURN INTERVAL SERIES MODEL FOR PERCOLATION ON SIERPINSKI CARPET LATTICE

Fractals ◽  
2013 ◽  
Vol 21 (03n04) ◽  
pp. 1350023 ◽  
Author(s):  
YANFANG DONG ◽  
JUN WANG
Keyword(s):  
Financial Time Series ◽  
Composite Index ◽  
Nonlinear Dependence ◽  
Fluctuation Analysis ◽  
Sierpinski Carpet ◽  
Financial Return ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Long Range Correlations ◽  
Return Interval ◽  
Sierpiński Carpet

A financial time series model is developed by the percolation system on the Sierpinski carpet lattice fractal. We investigate the fluctuation behaviors of various shuffled return interval series (original, randomly shuffled and by Zipf method) by applying the multifractal detrended fluctuation analysis for the financial model and Shanghai composite index. Numerically we show the fluctuations of the generalized Hurst exponents for different order parameters, the nonlinear dependence of these scaling exponents and the singularity spectrum show that the return intervals possess the multifractality. By comparing the MF-DFA empirical results of the original series to those for the randomly shuffled series, the empirical research exhibits the multifractality is mainly due to the contributions of long-range correlations as well as the broad probability density function. Further we show that the shuffled series by Zipf method exhibits the similar properties for the positive orders.

scholarly journals Price Appreciation and Roughness Duality in Bitcoin: A Multifractal Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2088
Author(s):  
Cristiana Vaz ◽  
Rui Pascoal ◽  
Helder Sebastião
Keyword(s):  
Fluctuation Analysis ◽  
Informational Efficiency ◽  
Comprehensive Overview ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Long Range Correlations ◽  
The Public ◽  
Long Run ◽  
Short Run ◽  
The Relationship

Since its launch in 2009, bitcoin has thrived, attracting the attention of investors, regulators, academia, and the public in general. Its price dynamics, characterized by extreme volatility, severe jumps, and impressive long-term appreciation, suggest that bitcoin is a new digital asset. This study presents a comprehensive overview of the fractality of bitcoin in a high-frequency framework, namely by applying Multifractal Detrended Fluctuation Analysis (MF-DFA) and a Multifractal Regime Detecting Method (MRDM) to Bitstamp 1 min bitcoin returns from January 2013 to July 2020. The results suggest that bitcoin is multifractal, with smaller and larger fluctuations being persistent and anti-persistent, respectively. Multifractality comes from significant long-range correlations, which cast some doubts on the informational efficiency at this frequency, but mainly comes from fat-tails, which highlights the significant risks undertaken by investors in this market. Our most important result is that the degree and richness of multifractality is time-varying and increased after 2017, when volumes and prices experienced an explosive behaviour. This complexity puts into perspective the duality of bitcoin: while it is characterized by long-run attractiveness and increasing valuation, it also has a high short-run instability. Hence, this study provides some empirical evidence supporting the relationship between these two observable features.

scholarly journals Meteorological Drought Monitoring in Northeastern China Using Multiple Indices

Water ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 72 ◽  
Author(s):  
Fengping Li ◽  
Hongyan Li ◽  
Wenxi Lu ◽  
Guangxin Zhang ◽  
Joo-Cheol Kim
Keyword(s):  
Standardized Precipitation Index ◽  
Meteorological Drought ◽  
Drought Monitoring ◽  
Drought Indices ◽  
Monthly Precipitation ◽  
Precipitation Data ◽  
Z Score ◽  
Predictive Values ◽  
Daily Precipitation Data ◽  
Precipitation Changes

Drought monitoring is one of the significant issues of water resources assessment. Multiple drought indices (DIs), including Percent of Normal (PN), Standardized Precipitation Index (SPI), statistical Z-Score, and Effective Drought Index (EDI) at 18 different timesteps were employed to evaluate the drought condition in Wuyuer River Basin (WRB), Northeast China. Daily precipitation data of 50 years (1960–2010) from three meteorological stations were used in this study. We found DIs with intermediate time steps (7 to 18 months) to have the highest predictive values for identifying droughts. And DIs exhibited a better similarity in the 12-month timestep. Among all the DIs, EDI exhibited the best correlation with other DIs for various timesteps. When further comparing with historical droughts, Z-Score, SPI, and EDI were found more sensitive to multi-monthly cumulative precipitation changes (r2 > 0.55) with respect to monthly precipitation changes (r2 ≤ 0.10), while EDI was more preferable when only monthly precipitation data were available. These results indicated that various indices for different timesteps should be investigated in drought monitoring in WRB, especially the intermediate timesteps should be considered.

scholarly journals IMPACT OF TANDEM REPEATS ON THE SCALING OF NUCLEOTIDE SEQUENCES

2006 ◽  
Vol 16 (10) ◽  
pp. 3103-3108
Author(s):  
RADHAKRISHNAN NAGARAJAN ◽  
MEENAKSHI UPRETI
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Tandem Repeats ◽  
Nucleotide Sequences ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Long Range Correlations ◽  
Reliable Estimation ◽  
Detrended Fluctuation

Techniques such as detrended fluctuation analysis (DFA) and its extensions have been widely used to determine the nature of scaling in nucleotide sequences. In this brief communication we show that tandem repeats which are ubiquitous in nucleotide sequences can prevent reliable estimation of possible long-range correlations. Therefore, it is important to investigate the presence of tandem repeats prior to scaling exponent estimation.

scholarly journals Drought Monitoring Based on Remote Sensing in a Grain-Producing Region in the Cerrado–Amazon Transition, Brazil

Water ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 3366
Author(s):  
Mairon Ânderson Cordeiro Correa de Carvalho ◽  
Eduardo Morgan Uliana ◽  
Demetrius David da Silva ◽  
Uilson Ricardo Venâncio Aires ◽  
Camila Aparecida da Silva Martins ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Standardized Precipitation Index ◽  
Meteorological Drought ◽  
Rain Gauge ◽  
Monthly Precipitation ◽  
Indirect Measurements ◽  
Study Region ◽  
Development Cycle ◽  
Historical Series ◽  
The Standardized Precipitation Index

Drought is a natural disaster that affects a country’s economy and food security. The monitoring of droughts assists in planning assertive actions to mitigate the resulting environmental and economic impacts. This work aimed to evaluate the performance of the standardized precipitation index (SPI) using rainfall data estimated by orbital remote sensing in the monitoring of meteorological drought in the Cerrado–Amazon transition region, Brazil. Historical series from 34 rain gauge stations, in addition to indirect measurements of monthly precipitation obtained by remote sensing using the products CHIRPS-2.0, PERSIANN-CDR, PERSIANN-CCS, PERSIANN, GPM-3IMERGMv6, and GPM-3IMERGDLv6, were used in this study. Drought events detected by SPI were related to a reduction in soybean production. The SPI calculated from the historical rain series estimated by remote sensing allowed monitoring droughts, enabling a high detailing of the spatial variability of droughts in the region, mainly during the soybean development cycle. Indirect precipitation measures associated with SPI that have adequate performance for detecting droughts in the study region were PERSIANN-CCS (January), CHIRPS-2.0 (February and November), and GPM-3IMERGMv6 (March, September, and December). The SPI and the use of precipitation data estimated by remote sensing are effective for characterizing and monitoring meteorological drought in the study region.

scholarly journals Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington’s disease

1997 ◽  
Vol 82 (1) ◽  
pp. 262-269 ◽  
Author(s):  
Jeffrey M. Hausdorff ◽  
Susan L. Mitchell ◽  
Renée Firtion ◽  
C. K. Peng ◽  
Merit E. Cudkowicz ◽  
...  
Keyword(s):  
Huntington's Disease ◽  
Huntington’S Disease ◽  
Elderly Subjects ◽  
Fluctuation Analysis ◽  
System Control ◽  
Scaling Exponent ◽  
Long Range Correlations ◽  
Healthy Elderly ◽  
Stride Interval ◽  
Young Subjects

Hausdorff, Jeffrey M., Susan L. Mitchell, Renée Firtion, C. K. Peng, Merit E. Cudkowicz, Jeanne Y. Wei, and Ary L. Goldberger. Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington’s disease. J. Appl. Physiol. 82(1): 262–269, 1997.—Fluctuations in the duration of the gait cycle (the stride interval) display fractal dynamics and long-range correlations in healthy young adults. We hypothesized that these stride-interval correlations would be altered by changes in neurological function associated with aging and certain disease states. To test this hypothesis, we compared the stride-interval time series of 1) healthy elderly subjects and young controls and of 2) subjects with Huntington’s disease and healthy controls. Using detrended fluctuation analysis, we computed α, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. The scaling exponent α was significantly lower in elderly subjects compared with young subjects (elderly: 0.68 ± 0.14; young: 0.87 ± 0.15; P < 0.003). The scaling exponent α was also smaller in the subjects with Huntington’s disease compared with disease-free controls (Huntington’s disease: 0.60 ± 0.24; controls: 0.88 ± 0.17; P < 0.005). Moreover, α was linearly related to degree of functional impairment in subjects with Huntington’s disease ( r = 0.78, P < 0.0005). These findings demonstrate that stride-interval fluctuations are more random (i.e., less correlated) in elderly subjects and in subjects with Huntington’s disease. Abnormal alterations in the fractal properties of gait dynamics are apparently associated with changes in central nervous system control.

scholarly journals Bivariate Frequency of Meteorological Drought in the Upper Minjiang River Based on Copula Function

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2056
Author(s):  
Fangling Qin ◽  
Tianqi Ao ◽  
Ting Chen
Keyword(s):  
Marginal Distribution ◽  
Standardized Precipitation Index ◽  
Meteorological Drought ◽  
Copula Function ◽  
Distribution Functions ◽  
Joint Probability Distribution ◽  
Drought Risk ◽  
Monthly Precipitation ◽  
Copula Functions ◽  
Minjiang River

Based on the Standardized Precipitation Index (SPI) and copula function, this study analyzed the meteorological drought in the upper Minjiang River basin. The Tyson polygon method is used to divide the research area into four regions based on four meteorological stations. The monthly precipitation data of four meteorological stations from 1966 to 2016 were used for the calculation of SPI. The change trend of SPI1, SPI3 and SPI12 showed the historical dry-wet evolution phenomenon of short-term humidification and long-term aridification in the study area. The major drought events in each region are counted based on SPI3. The results show that the drought lasted the longest in Maoxian region, the occurrence of minor drought events was more frequent than the other regions. Nine distribution functions are used to fit the marginal distribution of drought duration (D), severity (S) and peak (P) estimated based on SPI3, the best marginal distribution is obtained by chi-square test. Five copula functions are used to create a bivariate joint probability distribution, the best copula function is selected through AIC, the univariate and bivariate return periods were calculated. The results of this paper will help the study area to assess the drought risk.

FORECASTING SMOOTHED NON-STATIONARY TIME SERIES USING GENETIC ALGORITHMS

2007 ◽  
Vol 18 (06) ◽  
pp. 1071-1086 ◽  
Author(s):  
P. NOROUZZADEH ◽  
B. RAHMANI ◽  
M. S. NOROUZZADEH
Keyword(s):  
Genetic Algorithm ◽  
Time Series ◽  
Kernel Smoothing ◽  
Financial Time Series ◽  
Stationary Time Series ◽  
Time Variability ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Long Range Correlations ◽  
Smoothing Methods

We introduce kernel smoothing method to extract the global trend of a time series and remove short time scales variations and fluctuations from it. A multifractal detrended fluctuation analysis (MF-DFA) shows that the multifractality nature of TEPIX returns time series is due to both fatness of the probability density function of returns and long range correlations between them. MF-DFA results help us to understand how genetic algorithm and kernel smoothing methods act. Then we utilize a recently developed genetic algorithm for carrying out successful forecasts of the trend in financial time series and deriving a functional form of Tehran price index (TEPIX) that best approximates the time variability of it. The final model is mainly dominated by a linear relationship with the most recent past value, while contributions from nonlinear terms to the total forecasting performance are rather small.

scholarly journals Модифицированный метод флуктуационного анализа нестационарных процессов

2020 ◽  
Vol 46 (6) ◽  
pp. 47
Author(s):  
А.Н. Павлов ◽  
О.Н. Павлова ◽  
А.А. Короновский (мл.)
Keyword(s):  
Experimental Data ◽  
Blood Flow ◽  
Detrended Fluctuation Analysis ◽  
Quantitative Description ◽  
Fluctuation Analysis ◽  
Stationary Processes ◽  
Scaling Exponent ◽  
Long Range Correlations ◽  
Proposed Modification ◽  
Detrended Fluctuation

A method of detrended fluctuation analysis (DFA) is considered, which enables studying long-range correlations in non-stationary processes. Its modification is proposed that includes estimation of an additional quantity, namely, a scaling exponent characterizing the effects of non-stationarity in the experimental data. Using the dynamics of blood flow velocity in cerebral vessels as an example, the possibilities of a quantitative description of changes in the signal structure using the proposed modification of DFA are shown.

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