scholarly journals Long-Range Temporal Correlations, Multifractality, and the Causal Relation Between Neural Inputs and Movements

2011 ◽  
Author(s):  
Jianbo Gao ◽  
Yi Zheng ◽  
Jing Hu
Keyword(s):  
Factor Analysis ◽  
Long Range ◽  
Multifractal Analysis ◽  
Causal Relation ◽  
Fano Factor ◽  
Fluctuation Analysis ◽  
Movement Trajectory ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Reaching Task ◽  
Temporal Correlations

Understanding the causal relation between neural inputs and movements is very important for the success of brain machine interfaces (BMIs). In this study, we perform systematic statistical and information theoretical analysis of neuronal firings of 104 neurons, and employ three different types of fractal and multifractal techniques (including Fano factor analysis, multifractal detrended fluctuation analysis (MF-DFA), and wavelet multifractal analysis) to examine whether neuronal firings related to movements may have long-range temporal correlations. We find that MF-DFA and wavelet multifractal analysis (but not Fano factor analysis) clearly indicate that when neuronal firings are not well correlated with movement trajectory, they do not have or only have weak temporal correlations. When neuronal firings are well correlated with movements, they are characterized by very strong temporal correlations, up to a time scale comparable to the average time between two successive reaching tasks. This suggests that neurons well correlated with hand trajectory experienced a “re-setting” effect at the start of each reaching task. We further discuss the significance of the coalition of those important neurons in executing cortical control of prostheses.

scholarly journals Multifractal Analysis of Hydrologic Data Using Wavelet Methods and Fluctuation Analysis

2017 ◽  
Vol 2017 ◽  
pp. 1-18 ◽  
Author(s):  
Tongzhou Zhao ◽  
Liang Wu ◽  
Dehua Li ◽  
Yiming Ding
Keyword(s):  
Time Series ◽  
Water Level ◽  
Multifractal Analysis ◽  
Simulation Models ◽  
Northern China ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Wavelet Leaders ◽  
Detailed Characteristic ◽  
Wavelet Methods

We study the multifractal properties of water level with a high-frequency and massive time series using wavelet methods (estimation of Hurst exponents, multiscale diagram, and wavelet leaders for multifractal analysis (WLMF)) and multifractal detrended fluctuation analysis (MF-DFA). The dataset contains more than two million records from 10 observation sites at a northern China river. The multiscale behaviour is observed in this time series, which indicates the multifractality. This multifractality is detected via multiscale diagram. Then we focus on the multifractal analysis using MF-DFA and WLMF. The two methods give the same conclusion that at most sites the records satisfy the generalized binomial multifractal model, which is robust for different times (morning, afternoon, and evening). The variation in the detailed characteristic parameters of the multifractal model indicates that both human activities and tributaries influence the multifractality. Our work is useful for building simulation models of the water level of local rivers with many observation sites.

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.

A modified Multifractal Detrended Fluctuation Analysis (MFDFA) approach for multifractal analysis of precipitation

2021 ◽  
Vol 565 ◽  
pp. 125611
Author(s):  
Jorge Luis Morales Martínez ◽  
Ignacio Segovia-Domínguez ◽  
Israel Quiros Rodríguez ◽  
Francisco Antonio Horta-Rangel ◽  
Guillermo Sosa-Gómez
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Multifractal Analysis ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Detrended Fluctuation

MULTIFRACTAL BEHAVIORS IN FOREIGN EXCHANGE MARKETS

Fractals ◽  
2009 ◽  
Vol 17 (01) ◽  
pp. 15-21 ◽  
Author(s):  
SOO YONG KIM ◽  
GYUCHANG LIM ◽  
KI-HO CHANG ◽  
KUM LAN KIM ◽  
S. Y. LEE ◽  
...  
Keyword(s):  
Multifractal Analysis ◽  
Market Price ◽  
Underlying Mechanism ◽  
Fluctuation Analysis ◽  
Two Phase ◽  
Market Prices ◽  
Temporal Correlations ◽  
Developed Turbulence ◽  
Exchange Markets ◽  
Detrended Fluctuation

A two-phase phenomenon in three financial exchange prices is studied. To understand the underlying mechanism for the formation of market prices, we perform the multifractal analysis and the detrended fluctuation analysis in terms of time series of market prices. We also examine higher order temporal correlations for the market price. Although the multifractal properties of market prices are obtained, it cannot be reproduced the binomial multiplicative process through that was used to understand fully developed turbulence.

scholarly journals Comparative Multifractal Detrended Fluctuation Analysis of Heavy Ion Interactions at a Few GeV to a Few Hundred GeV

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Gopa Bhoumik ◽  
Argha Deb ◽  
Swarnapratim Bhattacharyya ◽  
Dipak Ghosh
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Heavy Ion ◽  
Projectile Energy ◽  
Fluctuation Analysis ◽  
Data Set ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Range Correlation ◽  
Multifractal Property ◽  
Detrended Fluctuation

We have studied the multifractality of pion emission process in16O-AgBr interactions at 2.1 AGeV  and  60 AGeV,12C-AgBr  and  24Mg-AgBr interactions at 4.5 AGeV, and32S-AgBr interactions at 200 AGeV using Multifractal Detrended Fluctuation Analysis (MFDFA) method which is capable of extracting the actual multifractal property filtering out the average trend of fluctuation. The analysis reveals that the pseudorapidity distribution of the shower particles is multifractal in nature for all the interactions; that is, pion production mechanism has inbuilt multiscale self-similarity property. We have employed MFDFA method for randomly generated events for32S-AgBr interactions at 200 AGeV. Comparison of expt. results with those obtained from randomly generated data set reveals that the source of multifractality in our data is the presence of long range correlation. Comparing the results obtained from different interactions, it may be concluded that strength of multifractality decreases with projectile mass for the same projectile energy and for a particular projectile it increases with energy. The values of ordinary Hurst exponent suggest that there is long range correlation present in our data for all the interactions.

MULTIFRACTAL DETRENDED FLUCTUATION ANALYSIS OF ELECTRIC LOAD SERIES

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550010 ◽  
Author(s):  
XIAOHUI YUAN ◽  
BIN JI ◽  
YANBIN YUAN ◽  
YUEHUA HUANG ◽  
XIANSHAN LI ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Quadratic Function ◽  
Fluctuation Analysis ◽  
Electric Load ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Range Correlation ◽  
Detrended Fluctuation ◽  
Multifractal Nature

Multifractal detrended fluctuation analysis (MF-DFA) method is applied to analyze the daily electric load time series. The results of the MF-DFA show that there are three crossover timescales at seven days, 15 days and 365 days approximately in the fluctuation function. Also we find that these fluctuations have multifractal nature with long range correlation behavior. The multifractal singularity spectrum of the daily electric load series has been fitted by the quadratic function model. Comparing the MF-DFA results of the original load series with those of shuffled and surrogate series, it concludes that the multifractal characteristics of the daily electric load time series is due to both broadness of the probability density function and long-range correlation, and the long-range correlation is dominant.

scholarly journals MONA LISA: THE STOCHASTIC VIEW AND FRACTALITY IN COLOR SPACE

2008 ◽  
Vol 19 (06) ◽  
pp. 855-866 ◽  
Author(s):  
POURIA PEDRAM ◽  
G. R. JAFARI
Keyword(s):  
Stochastic Process ◽  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Color Space ◽  
Statistical Properties ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Mona Lisa ◽  
Artistic Works ◽  
Detrended Fluctuation

A painting consists of objects which are arranged in specific ways. The art of painting is drawing the objects, which can be considered as known trends, in an expressive manner. Detrended methods are suitable for characterizing the artistic works of the painter by eliminating trends. It means that the study of paintings, regardless of its apparent purpose, as a stochastic process. Multifractal detrended fluctuation analysis is applied to characterize the statistical properties of Mona Lisa, as an instance, to exhibit the fractality of the painting. The results show that Mona Lisa is a long-range correlated and almost behaves similar in various scales.

Spatial rangeland variability: using summary statistics and multifractal analysis to classify and monitor rangelands.

2021 ◽  
Author(s):  
Ernesto Sanz ◽  
Andrés Almeida-Ñauñay ◽  
Carlos G. Diaz Ambrona ◽  
Antonio Saa-Requejo ◽  
Margarita Ruiz-Ramos ◽  
...  
Keyword(s):  
Land Surface ◽  
Multifractal Analysis ◽  
Vegetation Index ◽  
Absolute Difference ◽  
Fluctuation Analysis ◽  
Observation Data ◽  
Summary Statistics ◽  
Land Uses ◽  
Agricultural Insurance ◽  
Multifractal Detrended Fluctuation Analysis

<p>Rangelands ecosystem comprises more than a third of the global land surface, sustaining key ecosystem services and livelihoods. Unfortunately, they suffer from severe degradation on a global scale. Tailored-monitoring of rangeland will allow us to improve their management and maintain their social-ecological systems.</p> <p>MODIS data are commonly used to calculate Normalized Differenced Vegetation Index (NDVI) and NDVI anomaly (NDVIa) to monitor rangelands. In this study, we compare summary statistics and multifractal analysis to see if using complexity based tools improves our ability to differentiate land uses and types using remote sensing.</p> <p>We collected time series using satellite data of MODIS (MOD09Q1.006) from 2000 to 2019. An area from southeastern Spain (Murcia province) of 6.25 Km<sup>2</sup> was selected. This area comprised 132 pixels with a spatial resolution of 250 x 250 m<sup>2</sup> and a temporal resolution of 8 days. This area includes irrigated and rainfed crops, shrubs and forested patches.</p> <p>Multifractal detrended fluctuation analysis (MF-DFA) focuses on measuring variations of the moments of the absolute difference of their values at different scales. This allows us to use different multifractal exponent such as generalized Hurst exponent (H(q)), and its range (ΔH) to characterize the area. Here, we have selected H(1), H(2) and ΔH, to reflect variance, persistence and multifractality, respectively. Then, we compare them to the average, standard deviation and kurtosis of our NDVI and NDVIa series.</p> <p>Our results indicate that MF-DFA, allow us to see more clearly the differences among the pixels than the summary statistics. Particularly H(1) and H(2) of NDVI reflects more precisely the vegetation profile and land uses of the selected area. On the other hand, NDVIa allows us to highlight those pixels where several uses occur, or some feature such as roads interact with NDVI. MF-DFA appears as a promising tool to classify and monitor rangelands.</p> <p><strong>Acknowledgements: </strong>The authors acknowledge the support of Project No. PGC2018-093854-B-I00 of the Ministerio de Ciencia, Innovación y Universidades of Spain, “Garantía Juvenil” scholarship from Comunidad de Madrid, and the financial support from Boosting Agricultural Insurance based on Earth Observation data - BEACON project under agreement Nº 821964, funded under H2020EU, DT-SPACE-01-EO-2018-2020.</p>

Sign in / Sign up

Export Citation Format

Share Document