A probe into the Multifractal Behaviour of Total Ozone Time Series through Detrended Fluctuation Analysis

Total Ozone ◽

Fluctuation Analysis ◽

Order Polynomial ◽

Local Trend ◽

Detrended Fluctuation ◽

Daily Total

Abstract The present study reports a multifractal detrended fluctuation analysis of total ozone time series. Considering daily total ozone concentration (TOC) data ranging from 2015 to 2019, we have created a new profile by subtracting the trend. Subsequently we have divided the profile \({X}_{i}\) into non intersecting segments of equal time scale varying from 25 to 30. Fitting a second order polynomial, we have eliminated the local trend from each segment and thereafter we have computed the detrended variance. Finally the multifractal behaviour has been identified and the singularity spectra has helped us in obtaining the generalised Hurst exponent which in this case has come out to be greater than 0.5.

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

Symmetry ◽

10.3390/sym12071157 ◽

2020 ◽

Vol 12 (7) ◽

pp. 1157

Author(s):

Faheem Aslam ◽

Saima Latif ◽

Paulo Ferreira

Keyword(s):

Time Series ◽

Long Range ◽

Stock Markets ◽

Financial Time Series ◽

Long Range Dependence ◽

Fluctuation Analysis ◽

Financial Time ◽

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.

Performance of multifractal detrended fluctuation analysis on short time series

Physical Review E ◽

10.1103/physreve.87.022918 ◽

2013 ◽

Vol 87 (2) ◽

Cited By ~ 28

Author(s):

Juan Luis López ◽

Jesús Guillermo Contreras

Keyword(s):

Time Series ◽

Fluctuation Analysis ◽

Short Time Series ◽

Short Time ◽

Scaling behavior of earthquakes’ inter-events time series

Open Physics ◽

10.2478/s11534-009-0058-0 ◽

2009 ◽

Vol 7 (3) ◽

Cited By ~ 4

Author(s):

Shahriar Shadkhoo ◽

Fakhteh Ghanbarnejad ◽

Gholam Jafari ◽

Mohammad Tabar

Keyword(s):

Time Series ◽

Time Scales ◽

Hurst Exponent ◽

Fluctuation Analysis ◽

Data Set ◽

Scaling Properties ◽

Independent Events ◽

AbstractIn this paper, we investigate the statistical and scaling properties of the California earthquakes’ inter-events over a period of the recent 40 years. To detect long-term correlations behavior, we apply detrended fluctuation analysis (DFA), which can systematically detect and overcome nonstationarities in the data set at all time scales. We calculate for various earthquakes with magnitudes larger than a given M. The results indicate that the Hurst exponent decreases with increasing M; characterized by a Hurst exponent, which is given by, H = 0:34 + 1:53/M, indicating that for events with very large magnitudes M, the Hurst exponent decreases to 0:50, which is for independent events.

Multifractal Detrended Fluctuation Analysis of Interevent Time Series in a Modified OFC Model

Communications in Theoretical Physics ◽

10.1088/0253-6102/59/1/01 ◽

2013 ◽

Vol 59 (1) ◽

pp. 1-6 ◽

Cited By ~ 11

Author(s):

Min Lin ◽

Shuang-Xi Yan ◽

Gang Zhao ◽

Gang Wang

Keyword(s):

Time Series ◽

Fluctuation Analysis ◽

Interevent Time ◽

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

Canadian Journal of Physics ◽

10.1139/p10-039 ◽

2010 ◽

Vol 88 (8) ◽

pp. 545-551 ◽

Cited By ~ 14

Author(s):

Srimonti Dutta

Keyword(s):

Time Series ◽

Stock Market ◽

Nonstationary Time Series ◽

Anomalous Behaviour ◽

Fluctuation Analysis ◽

Indian Stock Market ◽

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.

Fish Sound Characterization Using Multifractal Detrended Fluctuation Analysis

Fluctuation and Noise Letters ◽

10.1142/s0219477520500091 ◽

2020 ◽

Vol 19 (01) ◽

pp. 2050009 ◽

Cited By ~ 1

Author(s):

Kranthikumar Chanda ◽

Shubham Shet ◽

Bishwajit Chakraborty ◽

Arvind K. Saran ◽

William Fernandes ◽

...

Keyword(s):

Hurst Exponent ◽

Linear Method ◽

Multifractal Spectrum ◽

Fluctuation Analysis ◽

Generalized Hurst Exponent ◽

Estuarine Systems ◽

Detrended Fluctuation ◽

Sound Data

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 [Formula: see text] values are found to be [Formula: see text] and [Formula: see text] for the fish families Batrachoididae (common name: Toadfish) and Sciaenidae (common name: Croakers, drums), respectively. The generalized Hurst exponent [Formula: see text]-related width parameters [Formula: see text] are found to be [Formula: see text] and [Formula: see text], 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.

MULTIFRACTAL DETRENDED FLUCTUATION ANALYSIS OF ELECTRIC LOAD SERIES

Fractals ◽

10.1142/s0218348x15500103 ◽

2015 ◽

Vol 23 (02) ◽

pp. 1550010 ◽

Cited By ~ 8

Author(s):

XIAOHUI YUAN ◽

BIN JI ◽

YANBIN YUAN ◽

YUEHUA HUANG ◽

XIANSHAN LI ◽

...

Keyword(s):

Time Series ◽

Long Range ◽

Quadratic Function ◽

Fluctuation Analysis ◽

Electric Load ◽

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.

Multifractal detrended fluctuation analysis of soil radon (222Rn) and thoron (220Rn) time series

Journal of Radioanalytical and Nuclear Chemistry ◽

10.1007/s10967-021-07650-x ◽

2021 ◽

Vol 328 (1) ◽

pp. 425-434

Author(s):

Muhammad Rafique ◽

Javid Iqbal ◽

Kashif Javed Lone ◽

Kimberlee Jane Kearfott ◽

Saeed Ur Rahman ◽

...

Keyword(s):

Time Series ◽

Fluctuation Analysis ◽

Soil Radon ◽

Target Detection within Sea Clutter Based on Multifractal Detrended Fluctuation Analysis

Advanced Engineering Forum ◽

10.4028/www.scientific.net/aef.4.259 ◽

2012 ◽

Vol 4 ◽

pp. 259-262 ◽

Cited By ~ 1

Author(s):

Zhan Xu ◽

Jian Wei Wan ◽

Gang Li ◽

Fang Su

Keyword(s):

Time Series ◽

Target Detection ◽

Hurst Parameter ◽

Fluctuation Analysis ◽

Sea Clutter ◽

Potential Applications ◽

Detrended Fluctuation ◽

Better Than

We present the multifractal detrended fluctuation analysis (MFDFA) for target detection within sea clutter. The multifractal character of the sea clutter time series is discussed. The great hurst parameter differences between sea clutter and target by the detrended fluctuation analysis are available. Experimental results of IPIX datasets show that the proposed method performs better than that based on fluctuation analysis (FA). This type of analysis is promising an efficient framework for analysis of sea radar signals with several potential applications.

Multifractal analysis of solar flare indices and their horizontal visibility graphs

Nonlinear Processes in Geophysics ◽

10.5194/npg-19-657-2012 ◽

2012 ◽

Vol 19 (6) ◽

pp. 657-665 ◽

Cited By ~ 12

Author(s):

Z. G. Yu ◽

V. Anh ◽

R. Eastes ◽

D.-L. Wang

Keyword(s):

Time Series ◽

Solar Cycle ◽

Multifractal Analysis ◽

Fluctuation Analysis ◽

Horizontal Visibility ◽

X Ray ◽

Visibility Graphs ◽

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.