scholarly journals A Modified Multifractal Detrended Fluctuation Analysis (MFDFA) Approach for Multifractal Analysis of Precipitation in Dongting Lake Basin, China

Water ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 891 ◽  
Author(s):  
Xike Zhang ◽  
Gui Zhang ◽  
Luo Qiu ◽  
Bo Zhang ◽  
Yurong Sun ◽  
...  
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Daily Precipitation ◽  
Dongting Lake ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Lake Basin ◽  
Precipitation Time Series ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Detrended Fluctuation

Multifractal detrended fluctuation analysis (MFDFA) method can examine higher-dimensional fractal and multifractal characteristics hidden in time series. However, removal of local trends in MFDFA is based on discontinuous polynomial fitting, resulting in pseudo-fluctuation errors. In this paper, we propose a two-stage modified MFDFA for multifractal analysis. First, an overlap moving window (OMW) algorithm is introduced to divide time series of the classic MFDFA method. Second, detrending by polynomial fitting local trend in traditional MFDFA is replaced by ensemble empirical mode decomposition (EEMD)-based local trends. The modified MFDFA is named OMW-EEMD-MFDFA. Then, the performance of the OMW-EEMD-MFDFA method is assessed by extensive numeric simulation experiments based on a p-model of multiplicative cascading process. The results show that the modified OMW-EEMD-MFDFA method performs better than conventional MFDFA and OMW-MFDFA methods. Lastly, the modified OMW-EEMD-MFDFA method is applied to explore multifractal characteristics and multifractal sources of daily precipitation time series data at the Mapoling and Zhijiang stations in Dongting Lake Basin. Our results showed that the scaling properties of the daily precipitation time series at the two stations presented a long-range correlation, showing a long-term persistence of the previous state. The strong q-dependence of H ( q ) and τ ( q ) indicated strong multifractal characteristics in daily precipitation time series data at the two stations. Positive Δ f values demonstrate that precipitation may have a local increasing trend. Comparing the generalized Hurst exponent and the multifractal strength of the original precipitation time series data with its shuffled and surrogate time series data, we found that the multifractal characteristics of the daily precipitation time series data were caused by both long-range correlations between small and large fluctuations and broad probability density function, but the broad probability density function was dominant. This study may be of practical and scientific importance in regional precipitation forecasting, extreme precipitation regulation, and water resource management in Dongting Lake Basin.

Modeling and forecasting multifractal wavelet scale: Western market versus eastern market

2018 ◽  
Vol 29 (11) ◽  
pp. 1850109 ◽  
Author(s):  
Emrah Oral ◽  
Gazanfer Unal
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
Price Change ◽  
Wavelet Coherence ◽  
Series Data ◽  
Primary Study ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Time Frequency

This leading primary study is about modeling multifractal wavelet scale time series data using multiple wavelet coherence (MWC), continuous wavelet transform (CWT) and multifractal detrended fluctuation analysis (MFDFA) and forecasting with vector autoregressive fractionally integrated moving average (VARFIMA) model. The data is acquired from Yahoo Finances!, which is composed of 1671 daily stock market of eastern (NIKKEI, TAIEX, KOPSI) and western (SP500, FTSE, DAX) markets. Once the co-movement dependencies on time-frequency space are determined with MWC, the coherent data is extracted out of raw data at a certain scale by using CWT. The multifractal behavior of the extracted series is verified by MFDFA and its local Hurst exponents have been calculated obtaining root mean square of residuals at each scale. This inter-calculated fluctuation function time series has been re-scaled and used to estimate the process with VARFIMA model and forecasted accordingly. The results have shown that the direction of price change is determined without difficulty and the efficiency of forecasting has been substantially increased using highly correlated multifractal wavelet scale time series data.

scholarly journals DETRENDED FLUCTUATION ANALYSIS OF THE TCP-RED ALGORITHM

2009 ◽  
Vol 19 (12) ◽  
pp. 4237-4245 ◽  
Author(s):  
XI CHEN ◽  
SIU-CHUNG WONG ◽  
CHI K. TSE ◽  
LJILJANA TRAJKOVIĆ
Keyword(s):  
Time Series ◽  
Long Range ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Time Series Data ◽  
Analytical Models ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Detrended Fluctuation

It has been observed that Internet gateways employing Transport Control Protocol (TCP) and the Random Early Detection (RED) control algorithm may exhibit instability and oscillatory behavior. Most control methods proposed in the past have been based on analytical models that rely on statistical measurements of network parameters. In this paper, we apply the detrended fluctuation analysis (DFA) method to analyze stability of the TCP-RED system. The DFA is used to analyze time-series data and generate power-law scaling exponents, which indicate the long-range correlations of the time series. We quantify the stability of the TCP-RED system by examining the variation of the DFA power-law scaling exponent when the system parameters are varied. We also study the long-range power-law correlations of TCP window periods.

A new approach to detect extreme events: a case study using remotely-sensed precipitation time-series data

2021 ◽  
Vol 24 ◽  
pp. 100618
Author(s):  
Philipe Riskalla Leal ◽  
Ricardo José de Paula Souza e Guimarães ◽  
Fábio Dall Cortivo ◽  
Rayana Santos Araújo Palharini ◽  
Milton Kampel
Keyword(s):  
Time Series ◽  
Extreme Events ◽  
Time Series Data ◽  
Remotely Sensed ◽  
Series Data ◽  
Precipitation Time Series ◽  
New Approach

scholarly journals Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1157
Author(s):  
Faheem Aslam ◽  
Saima Latif ◽  
Paulo Ferreira
Keyword(s):  
Time Series ◽  
Long Range ◽  
Stock Markets ◽  
Detrended Fluctuation Analysis ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Financial Time ◽  
Detrended Fluctuation

The use of multifractal approaches has been growing because of the capacity of these tools to analyze complex properties and possible nonlinear structures such as those in financial time series. This paper analyzes the presence of long-range dependence and multifractal parameters in the stock indices of nine MSCI emerging Asian economies. Multifractal Detrended Fluctuation Analysis (MFDFA) is used, with prior application of the Seasonal and Trend Decomposition using the Loess (STL) method for more reliable results, as STL separates different components of the time series and removes seasonal oscillations. We find a varying degree of multifractality in all the markets considered, implying that they exhibit long-range correlations, which could be related to verification of the fractal market hypothesis. The evidence of multifractality reveals symmetry in the variation trends of the multifractal spectrum parameters of financial time series, which could be useful to develop portfolio management. Based on the degree of multifractality, the Chinese and South Korean markets exhibit the least long-range dependence, followed by Pakistan, Indonesia, and Thailand. On the contrary, the Indian and Malaysian stock markets are found to have the highest level of dependence. This evidence could be related to possible market inefficiencies, implying the possibility of institutional investors using active trading strategies in order to make their portfolios more profitable.

scholarly journals Long-Range Correlations and Characterization of Financial and Volcanic Time Series

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 441 ◽  
Author(s):  
Maria C. Mariani ◽  
Peter K. Asante ◽  
Md Al Masum Bhuiyan ◽  
Maria P. Beccar-Varela ◽  
Sebastian Jaroszewicz ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Time Series Data ◽  
Financial Time Series ◽  
Seismic Station ◽  
Volcanic Eruptions ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Properties ◽  
Long Range Correlations

In this study, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data have high frequencies. The objective is to determine whether they follow a Gaussian or Lévy distribution, as well as establish the existence of long-range correlations in these time series. The results obtained from the DEA technique are compared with the Hurst R/S analysis and Detrended Fluctuation Analysis (DFA) methodologies. We conclude that these methodologies are effective in classifying the high frequency financial indices and volcanic eruption data—the financial time series can be characterized by a Lévy walk while the volcanic time series is characterized by a Lévy flight.

scholarly journals Scale Analysis and Correlation Study of Wildfire and the Meteorological Factors That Influence It

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Jiazheng Lu ◽  
Tejun Zhou ◽  
Bo Li ◽  
Chuanping Wu
Keyword(s):  
Time Series ◽  
Time Scale ◽  
Detrended Fluctuation Analysis ◽  
Cross Correlation ◽  
Daily Precipitation ◽  
Meteorological Factors ◽  
Fluctuation Analysis ◽  
Average Temperature ◽  
Cross Correlation Analysis ◽  
Detrended Fluctuation

Wildfire is a large-scale complex system. Insight into the mechanism that drives wildfires can be revealed by the distribution of the wildfire over a large time scale, which is one of the important topics in wildfire research. In this study, the scaling properties of four meteorological factors (relative humidity, daily precipitation, daily average temperature, and maximum wind speed) that can affect wildfires (number of wildfires per day) were investigated by using the detrended fluctuation analysis method. The results showed that the time series for these meteorological factors and wildfires have similar power exponents and turning points for the power exponents curve. The five types of time series have a lasting and steady long-range power law correlation over a certain time scale range, where the corresponding exponents were 0.6484, 0.5724, 0.8647, 0.7344, and 0.6734, respectively. They also have a reversible long-range power law correlation beyond a certain time scale, where the corresponding exponents are 0.3862, 0.2218, 0.1372, 0.2621, and 0.2678. The multifractal detrended fluctuation analysis results showed that the wildfire time series were multifractal. The results of the research based on the detrended cross-correlation analysis and the multifractal detrended cross-correlation analysis showed that relative humidity and daily precipitation have a considerable impact on the wildfire time series, while the impacts of daily average temperature and the maximum wind speed are relatively small. This study showed that identifying the factors causing the inherent volatility in the wildfire time series can improve understanding of the dynamic mechanism controlling wildfires and the meteorological parameters. These results can also be used to quantify the correlation between wildfire and the meteorological factors investigated in this study.

scholarly journals Fractal Complexity of Daily Physical Activity Patterns Differs With Age Over the Life Span and Is Associated With Mortality in Older Adults

2018 ◽  
Vol 74 (9) ◽  
pp. 1461-1467 ◽  
Author(s):  
David A Raichlen ◽  
Yann C Klimentidis ◽  
Chiu-Hsieh Hsu ◽  
Gene E Alexander
Keyword(s):  
Physical Activity ◽  
Older Adults ◽  
Time Series ◽  
Time Scales ◽  
Mortality Risk ◽  
Time Series Data ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Wide Range ◽  
Wearable Accelerometers

Abstract Background Accelerometers are included in a wide range of devices that monitor and track physical activity for health-related applications. However, the clinical utility of the information embedded in their rich time-series data has been greatly understudied and has yet to be fully realized. Here, we examine the potential for fractal complexity of actigraphy data to serve as a clinical biomarker for mortality risk. Methods We use detrended fluctuation analysis (DFA) to analyze actigraphy data from the National Health and Nutrition Examination Survey (NHANES; n = 11,694). The DFA method measures fractal complexity (signal self-affinity across time-scales) as correlations between the amplitude of signal fluctuations in time-series data across a range of time-scales. The slope, α, relating the fluctuation amplitudes to the time-scales over which they were measured describes the complexity of the signal. Results Fractal complexity of physical activity (α) decreased significantly with age (p = 1.29E−6) and was lower in women compared with men (p = 1.79E−4). Higher levels of moderate-to-vigorous physical activity in older adults and in women were associated with greater fractal complexity. In adults aged 50–79 years, lower fractal complexity of activity (α) was associated with greater mortality (hazard ratio = 0.64; 95% confidence interval = 0.49–0.82) after adjusting for age, exercise engagement, chronic diseases, and other covariates associated with mortality. Conclusions Wearable accelerometers can provide a noninvasive biomarker of physiological aging and mortality risk after adjusting for other factors strongly associated with mortality. Thus, this fractal analysis of accelerometer signals provides a novel clinical application for wearable accelerometers, advancing efforts for remote monitoring of physiological health by clinicians.

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