Identification of Chaos-Periodic Transitions, Band Merging, and Internal Crisis Using Wavelet-DFA Method

2016 ◽  
Vol 26 (04) ◽  
pp. 1650065 ◽  
Author(s):  
Mahsa Vaghefi ◽  
Ali Motie Nasrabadi ◽  
Seyed Mohammad Reza Hashemi Golpayegani ◽  
Mohammad Reza Mohammadi ◽  
Shahriar Gharibzadeh
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Period Doubling ◽  
Nonstationary Time Series ◽  
The Self ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Analysis Method ◽  
Self Similarity ◽  
Self Similar ◽  
Detrended Fluctuation

Detrended Fluctuation Analysis (DFA) is a scaling analysis method that can identify intrinsic self-similarity in any nonstationary time series. In contrast, Wavelet Transform (WT) method is widely used to investigate the self-similar processes, as the self-similarity properties exist within the subbands. Therefore, a combination of these two approaches, DFA and WPT, is promising for rigorous investigation of such a system. In this paper a new methodology, so-called wavelet DFA, is introduced and interpreted to evaluate this idea. This approach, further than identifying self-similarity properties, enable us to detect and capture the chaos-periodic transitions, band merging, and internal crisis in systems that become chaotic through period-doubling phenomena. Changes of wavelet DFA exponent have been compared with that of Lyapunov and DFA through Logistic, Sine, Gaussian, Cubic, and Quartic Maps. Furthermore, the potential capabilities of this new exponent have been presented.

scholarly journals Effects of Exponential Trends on Correlations of Stock Markets

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Ai-Jing Lin ◽  
Peng-Jian Shang ◽  
Hua-Chun Zhou
Keyword(s):  
Time Series ◽  
Empirical Study ◽  
Long Range ◽  
Lower Order ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Analysis Method ◽  
Long Range Correlations ◽  
Detrended Fluctuation

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in time series. In this paper, DFA is employed to discuss the long-range correlations of stock market. The effects of exponential trends on correlations of Hang Seng Index (HSI) are investigated with emphasis. We find that the long-range correlations and the positions of the crossovers of lower order DFA appear to have no immunity to the additive exponential trends. Further, our analysis suggests that an increase in the DFA order increases the efficiency of eliminating on exponential trends. In addition, the empirical study shows that the correlations and crossovers are associated with DFA order and magnitude of exponential trends.

scholarly journals Multifractal analysis for the ULF geomagnetic data during the 1993 Guam earthquake

2005 ◽  
Vol 12 (2) ◽  
pp. 157-162 ◽  
Author(s):  
Y. Ida ◽  
M. Hayakawa ◽  
A. Adalev ◽  
K. Gotoh
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Multifractal Analysis ◽  
Fluctuation Analysis ◽  
Sensitive Parameter ◽  
Wide Range ◽  
Geomagnetic Data ◽  
Self Similar ◽  
Significant Change ◽  
Detrended Fluctuation

Abstract. In our previous papers we have shown that the fractal (monofractal) dimension (Do) showed a significant increase before the Guam earthquake occurred on 8 August, 1993. In order to have a further support to this precursory effect to the general rupture (earthquake) we have carried out the corresponding multifractal analysis (by means of detrended fluctuation analysis) for the same data to study the statistical self-similar properties in a wide range of scales. We have analyzed the ULF geomagnetic data (the most intense H component) observed at Guam observatory. As the result, we have found that we could observe significant changes in the multifractal parameters at Guam such that αmin showed a meaningful decrease about 25 days before the earthquake and correspondingly Δα increased because αmax exhibited no significant change at all. The most sensitive parameter seems to be non-uniformity factor Δ. Correspondingly, the generalized multifractal dimension Dq (q>1) showed a significant decrease (whereas Dq (q<0) showed no change) and D0 (=Dq (q=0) (as already found in our previous papers) is reconfirmed to increase before the earthquake. These multifractal characteristics seem to be a further support that these changes are closely associated with the earthquake as a precursor to the Guam earthquake, providing us with appreciable information on the pre-rupture evolution of the earthquake.

scholarly journals Investigating EEG Signals of Autistic Individuals Using Detrended Fluctuation Analysis

2021 ◽  
Vol 38 (5) ◽  
pp. 1515-1520
Author(s):  
Menaka Radhakrishnan ◽  
Karthik Ramamurthy ◽  
Avantika Kothandaraman ◽  
Gauri Madaan ◽  
Harini Machavaram
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Autism Spectrum ◽  
Brain Diseases ◽  
Fluctuation Analysis ◽  
Typically Developing ◽  
Eeg Signals ◽  
Self Similarity ◽  
Detrended Fluctuation ◽  
Electroencephalogram Eeg ◽  
The Brain

To record all electrical activity of the human brain, an electroencephalogram (EEG) test using electrodes attached to the scalp is conducted. Analysis of EEG signals plays an important role in the diagnosis and treatment of brain diseases in the biomedical field. One of the brain diseases found in early ages include autism. Autistic behaviours are hard to distinguish, varying from mild impairments, to intensive interruption in daily life. The non-linear EEG signals arising from various lobes of the brain have been studied with the help of a robust technique called Detrended Fluctuation Analysis (DFA). Here, we study the EEG signals of Typically Developing (TD) and children with Autism Spectrum Disorder (ASD) using DFA. The Hurst exponents, which are the outputs of DFA, are used to find out the strength of self-similarity in the signals. Our analysis works towards analysing if DFA can be a helpful analysis for the early detection of ASD.

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.

scholarly journals Fractal scaling analysis of groundwater dynamics in confined aquifers

2017 ◽  
Vol 8 (4) ◽  
pp. 931-949 ◽  
Author(s):  
Tongbi Tu ◽  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Time Series ◽  
Groundwater Level ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Fractal Scaling ◽  
Groundwater Level Fluctuations ◽  
Groundwater Dynamics ◽  
Detrended Fluctuation ◽  
Infinite Moments

Abstract. Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

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