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.

scholarly journals Fractal Scaling Analysis of Groundwater Dynamics in Confined Aquifers

2017 ◽  
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 hydro-climatic 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 of 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, which can model both the long-memory behavior as well as the Brownian finite-memory behavior.

Scaling analysis of hyperchaotic time series

2017 ◽  
Vol 28 (07) ◽  
pp. 1750094 ◽  
Author(s):  
J. S. Murguía
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Dynamical Evolution ◽  
Fluctuation Analysis ◽  
Discrete Wavelet ◽  
Scaling Analysis ◽  
Detrended Fluctuation ◽  
Hyperchaotic Systems

The time series of the states of several well-known hyperchaotic systems are analyzed numerically using the detrended fluctuation analysis based on the discrete wavelet transform. We report the finding of significant scaling behaviors (power-law like) in some of these time series, which can be used as an additional characteristic distinguishing the dynamical evolution of such systems.

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 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 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
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