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 Multifractal analysis of solar flare indices and their horizontal visibility graphs

2012 ◽  
Vol 19 (6) ◽  
pp. 657-665 ◽  
Author(s):  
Z. G. Yu ◽  
V. Anh ◽  
R. Eastes ◽  
D.-L. Wang
Keyword(s):  
Time Series ◽  
Solar Cycle ◽  
Detrended Fluctuation Analysis ◽  
Multifractal Analysis ◽  
Fluctuation Analysis ◽  
Horizontal Visibility ◽  
Multifractal Detrended Fluctuation Analysis ◽  
X Ray ◽  
Visibility Graphs ◽  
Detrended Fluctuation

Abstract. The multifractal properties of the daily solar X-ray brightness, Xl and Xs, during the period from 1 January 1986 to 31 December 2007 which includes two solar cycles are examined using the universal multifractal approach and multifractal detrended fluctuation analysis. Then we convert these time series into networks using the horizontal visibility graph technique. Multifractal analysis of the resulting networks is performed using an algorithm proposed by us. The results from the multifractal analysis show that multifractality exists in both raw daily time series of X-ray brightness and their horizontal visibility graphs. It is also found that the empirical K(q) curves of raw time series can be fitted by the universal multifractal model. The numerical results on the raw data show that the Solar Cycle 23 is weaker than the Solar Cycle 22 in multifractality. The values of h(2) from multifractal detrended fluctuation analysis for these time series indicate that they are stationary and persistent, and the correlations in the time series of Solar Cycle 23 are stronger than those for Solar Cycle 22. Furthermore, the multifractal scaling for the networks of the time series can reflect some properties which cannot be picked up by using the same analysis on the original time series. This suggests a potentially useful method to explore geophysical data.

THE EFFICIENCY OF SIN STOCKS: A MULTIFRACTAL ANALYSIS OF DRUG INDICES

2021 ◽  
pp. 1-22
Author(s):  
Faheem Aslam ◽  
Paulo Ferreira ◽  
Fahd Amjad ◽  
Haider Ali
Keyword(s):  
Time Series ◽  
Market Efficiency ◽  
Detrended Fluctuation Analysis ◽  
Multifractal Analysis ◽  
Fluctuation Analysis ◽  
Self Similarity ◽  
Multifractal Detrended Fluctuation Analysis ◽  
The North ◽  
Daily Data ◽  
Detrended Fluctuation

This study provides the first evidence of market efficiency of drug indices, especially cannabis and tobacco, which are known in finance as sin markets. The multifractal detrended fluctuation analysis (MFDFA) is employed on the daily data of six cannabis and one tobacco indices in order to measure efficiency by quantifying the intensity of self-similarity. The findings confirm multifractality in all sample series. Interestingly, Dow Jones Tobacco (DJUSTB) Index shows the highest multifractality, demonstrating the lowest efficiency, whereas S&P/TSX Cannabis (SPTXCAN) Index is the most efficient of all the time series under analysis, with the lowest multifractality levels. Only the North American Marijuana (NAMMAR), Cannabis World Index Gross Total Return (CANWLDGR) and DJUSTB show persistent behavior. These findings could be of interest to policymakers and regulators to establish new reforms to improve the efficiency of these markets, as well as for actual and potential investors.

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

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.

Multifractal analysis of velocity and temperature fluctuations in the atmospheric surface layer

2020 ◽  
Author(s):  
Ganapati Sahoo ◽  
Soumak Bhattacharjee ◽  
Timo Vesala ◽  
Rahul Pandit
Keyword(s):  
Time Series ◽  
Turbulent Flows ◽  
Detrended Fluctuation Analysis ◽  
Multifractal Analysis ◽  
Temperature Time Series ◽  
Temperature Fields ◽  
Fluctuation Analysis ◽  
Fluid Turbulence ◽  
Detrended Fluctuation ◽  
Temperature Time

<p>The characterization of the structure of non-stationary, noisy fluctuations in a time series, e.g., the time series of the velocity components or temperature in turbulent flows, is a problem of central importance in fluid dynamics, nonequilibrium statistical mechanics, atmospheric physics and climate science. Over the past few decades, a variety of statistical techniques, like detrended fluctuation analysis (DFA), have been used to reveal intricate, multiscaling properties of such time series. We present an analysis of velocity and temperature time series, which have been obtained by measurements over the canopy of Hyytiälä Forest in Finland.<br>In our study we use DFA, its generalization, namely, multifractal detrended fluctuation analysis (MFDFA), and the recently developed multiscale multifractal analysis (MMA), which is an extension of MFDFA. These methods allow us to characterize the rich hierarchy or multi- fractality of the dynamics of the time series of the velocity components and the temperature. In particular, we can clearly distinguish these time series from white noise and the signals that display simple, monofractal, scaling with a single exponent (also called the Hurst exponent). It is useful to recall that monofractal scaling is predicted for fluid turbulence at the level of the Kolmogorov’s phenomenological approach of 1941 (K41); experiments and direct numerical simulations suggest that three-dimensional (3D) fluid turbulence must be characterised by a hierarchy of exponents for it is truly multifractal.</p><p>We present an analysis of multifractality of velocity and temperature fields that have been measured, at different heights, over the canopy of Hyytiälä Forest in Finland. In particular, we carry out a detailed study of velocity and temperature time series by using MFDFA and MMA. Results from both these methods are consistent, as they must be; but, of course, the MMA results contain more information because they account for the dependence of the multifractality on the time intervals.</p>

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.

Multifractal detrended fluctuation analysis of SENSEX fluctuation in the Indian stock market

2010 ◽  
Vol 88 (8) ◽  
pp. 545-551 ◽  
Author(s):  
Srimonti Dutta
Keyword(s):  
Time Series ◽  
Stock Market ◽  
Detrended Fluctuation Analysis ◽  
Nonstationary Time Series ◽  
Anomalous Behaviour ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Indian Stock Market ◽  
Detrended Fluctuation

The fluctuation of SENSEX in the Indian stock market for the period Jan 2003–Dec 2009 is studied using the multifractal detrended fluctuation analysis (MFDFA) approach. The effect of the fall in the stock market in 2008 is also investigated. The data exhibits that the nonstationary time series of SENSEX fluctuations are multifractal in nature. An increase in the degree of multifractality prior to the anomalous behaviour in the SENSEX values is also observed. The increase in the degree of correlation for the period 2007–2009 is also responsible for the meteoric rise and the catastrophic fall in the values of SENSEX.

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