scholarly journals Self-Similar Models: Relationship between the Diffusion Entropy Analysis, Detrended Fluctuation Analysis and Lévy Models

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1046
Author(s):  
Maria C. Mariani ◽  
William Kubin ◽  
Peter K. Asante ◽  
Osei K. Tweneboah ◽  
Maria P. Beccar-Varela ◽  
...  
Keyword(s):  
Time Series ◽  
Lévy Process ◽  
Memory Effects ◽  
Levy Process ◽  
Fluctuation Analysis ◽  
Diffusion Entropy ◽  
Scaling Methods ◽  
Scaling Parameters ◽  
Self Similar ◽  
Detrended Fluctuation

Financial and geophysical data, like many other low and high frequency time series, are known to exhibit some memory effects. These memory effects may be long or short, permanent or temporal depending on the event that is being modeled. The purpose of this study is to investigate the memory effects characterized by the financial market closing values and volcanic eruption time series as well as to investigate the relation between the self-similar models used and the Lévy process. This paper uses highly effective scaling methods including Lévy processes, Detrended Fluctuation Analysis (DFA) and Diffusion Entropy Analysis (DEA) to examine long-range persistence behavior in time series by estimating their respective parameters. We use the parameter of the Lévy process (α) characterizing the data and the scaling parameters of DFA (H) and DEA (δ) characterizing the self-similar property to generate a relationship between the three (3) aforementioned scaling methods. Findings from the numerical simulations confirm the existence of long-range persistence (long-memory behavior) in both the financial and geophysical time series. Furthermore, the numerical results from this study indicates an approximate inverse relationship between the parameter of the Lévy process and the scaling parameters of the DFA and DEA (i.e., H , δ ≈ 1 α ), which we prove analytically.

scholarly journals MULTIFRACTAL ANALYSIS OF STRESS TIME SERIES DURING ULTRATHIN LUBRICANT FILM MELTING

2010 ◽  
Vol 09 (01) ◽  
pp. 19-35 ◽  
Author(s):  
ALEXEI V. KHOMENKO ◽  
IAKOV A. LYASHENKO ◽  
VADIM N. BORISYUK
Keyword(s):  
Time Series ◽  
Power Law ◽  
Lubricant Film ◽  
Fluctuation Analysis ◽  
Power Law Distribution ◽  
Stick Slip ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Flat Surfaces ◽  
Self Similar ◽  
Detrended Fluctuation

Melting of an ultrathin lubricant film confined between two atomically flat surfaces is studied using the rheological model for viscoelastic matter approximation. Phase diagram with domains, corresponding to sliding, dry, and two types of stick-slip friction regimes has been built taking into account additive noises of stress, strain, and temperature of the lubricant. The stress time series have been obtained for all regimes of friction using the Stratonovich interpretation. It has been shown that self-similar regime of lubricant melting is observed when intensity of temperature noise is much larger than intensities of strain and stress noises. This regime is defined by homogenous distribution, at which characteristic stress scale is absent. We study stress time series obtained for all friction regimes using multifractal detrended fluctuation analysis. It has been shown that multifractality of these series is caused by different correlations that are present in the system and also by a power-law distribution. Since the power-law distribution is related to small stresses, this case corresponds to self-similar solid-like lubricant.

scholarly journals AUTOMATICALLY DETECTING "SIGNIFICANT EVENTS" ON SenseCam

2013 ◽  
Vol 11 (06) ◽  
pp. 1350050 ◽  
Author(s):  
NA LI ◽  
MARTIN CRANE ◽  
HEATHER J. RUSKIN
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Time Windows ◽  
Fluctuation Analysis ◽  
Discrete Wavelet ◽  
Dominant Eigenvalue ◽  
Multiple Time ◽  
Correlation Relationship ◽  
Significant Events ◽  
Detrended Fluctuation

SenseCam is an effective memory-aid device that can automatically record images and other data from the wearer's whole day. The main issue is that, while SenseCam produces a sizeable collection of images over the time period, the vast quantity of captured data contains a large percentage of routine events, which are of little interest to review. In this article, the aim is to detect "Significant Events" for the wearers. We use several time series analysis methods such as Detrended Fluctuation Analysis (DFA), Eigenvalue dynamics and Wavelet Correlations to analyse the multiple time series generated by the SenseCam. We show that Detrended Fluctuation Analysis exposes a strong long-range correlation relationship in SenseCam collections. Maximum Overlap Discrete Wavelet Transform (MODWT) was used to calculate equal-time Correlation Matrices over different time scales and then explore the granularity of the largest eigenvalue and changes of the ratio of the sub-dominant eigenvalue spectrum dynamics over sliding time windows. By examination of the eigenspectrum, we show that these approaches enable detection of major events in the time SenseCam recording, with MODWT also providing useful insight on details of major events. We suggest that some wavelet scales (e.g., 8 minutes–16 minutes) have the potential to identify distinct events or activities.

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.

(MULTI)FRACTALITY OF PHYSIOLOGICAL TIME-SERIES

2006 ◽  
Vol 16 (07) ◽  
pp. 2103-2110 ◽  
Author(s):  
ANDREA KNEŽEVIĆ ◽  
MLADEN MARTINIS
Keyword(s):  
Physical Activity ◽  
Time Series ◽  
Angina Pectoris ◽  
Stable Angina ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Stable Angina Pectoris ◽  
Nonlinear Methods ◽  
Rr Interval ◽  
Detrended Fluctuation

This paper contains the application of fractal concept in analyzing heartbeat (RR interval) fluctuations measured under controlled physical activity for subjects with stable angina pectoris (SAP). Results that illustrate the separation ability of the nonlinear methods, such as the Hurst R/S method, the detrended fluctuation analysis, DFA, and the method of G-moments, in distinguishing healthy from SAP subjects in scaling parameter space are presented.

The scaling of time series size towards detrended fluctuation analysis

2016 ◽  
Vol 27 (11) ◽  
pp. 1650138
Author(s):  
Xiaolei Gao ◽  
Liwei Ren ◽  
Pengjian Shang ◽  
Guochen Feng
Keyword(s):  
Time Series ◽  
Stock Returns ◽  
Detrended Fluctuation Analysis ◽  
Finite Size ◽  
Finite Size Effect ◽  
Fluctuation Analysis ◽  
Exponential Relationship ◽  
Significant Information ◽  
Sequence Segmentation ◽  
Detrended Fluctuation

In this paper, we introduce a modification of detrended fluctuation analysis (DFA), called multivariate DFA (MNDFA) method, based on the scaling of time series size [Formula: see text]. In traditional DFA method, we obtained the influence of the sequence segmentation interval [Formula: see text], and it inspires us to propose a new model MNDFA to discuss the scaling of time series size towards DFA. The effectiveness of the procedure is verified by numerical experiments with both artificial and stock returns series. Results show that the proposed MNDFA method contains more significant information of series compared to traditional DFA method. The scaling of time series size has an influence on the auto-correlation (AC) in time series. For certain series, we obtain an exponential relationship, and also calculate the slope through the fitting function. Our analysis and finite-size effect test demonstrate that an appropriate choice of the time series size can avoid unnecessary influences, and also make the testing results more accurate.

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 The detrended fluctuation analysis of heartbeat intervals in time series during stress tests

2019 ◽  
Author(s):  
Amparo Salcedo-Martínez ◽  
Nancy Gabriela Pérez-López ◽  
José Alberto Zamora-Justo ◽  
Gonzalo Gálvez-Coyt ◽  
Alejandro Muñoz-Diosdado
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Stress Tests ◽  
Detrended Fluctuation

scholarly journals Time-Scaling Properties of Sunshine Duration Based on Detrended Fluctuation Analysis over China

Atmosphere ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 83 ◽  
Author(s):  
Lei Jiang ◽  
Jiping Zhang ◽  
Yan Fang
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Sunshine Duration ◽  
Underlying Surface ◽  
Fluctuation Analysis ◽  
Scaling Properties ◽  
Long Range Correlations ◽  
Time Scaling ◽  
Daily Sunshine ◽  
Detrended Fluctuation

The spatial and temporal variabilities of the daily Sunshine Duration (SSD) time series from the Chinese Meteorological Administration during the 1954–2009 period are examined by the Detrended Fluctuation Analysis (DFA) method. As a whole, weak long-range correlations (LRCs) are found in the daily SSD anomaly records over China. LRCs are also verified by shuffling the SSD records. The proportion of the stations with LRCs accounts for about 97% of the total. Many factors affect the scaling properties of the daily SSD records such as sea-land difference and Tibetan Plateau landform and so on. We find land use and land cover as one of the important factors closely links to LRCs of the SSD. Strong LRCs of the SSD mainly happen in underlying surface of deserts and crops, while weak LRCs occur in forest and grassland. Further studies of scaling behaviors are still necessary to be performed due to the complex underlying surface and climate system.

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