scholarly journals On the scaling ranges of detrended fluctuation analysis for long-term memory correlated short series of data

2013 ◽  
Vol 392 (10) ◽  
pp. 2384-2397 ◽  
Author(s):  
Dariusz Grech ◽  
Zygmunt Mazur
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Long Term Memory ◽  
Fluctuation Analysis ◽  
Term Memory ◽  
Short Series ◽  
Detrended Fluctuation

Scaling behavior of earthquakes’ inter-events time series

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Shahriar Shadkhoo ◽  
Fakhteh Ghanbarnejad ◽  
Gholam Jafari ◽  
Mohammad Tabar
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Hurst Exponent ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Data Set ◽  
Scaling Properties ◽  
Independent Events ◽  
Detrended Fluctuation

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.

scholarly journals A Demonstration of Long-Term Memory and Climate Predictability

2010 ◽  
Vol 23 (18) ◽  
pp. 5021-5029 ◽  
Author(s):  
Xiuhua Zhu ◽  
Klaus Fraedrich ◽  
Zhengyu Liu ◽  
Richard Blender
Keyword(s):  
Circulation Model ◽  
Ocean Model ◽  
Long Term Memory ◽  
Fluctuation Analysis ◽  
Global Circulation Model ◽  
Max Planck ◽  
Potential Predictability ◽  
Term Memory ◽  
Climate Predictability

Abstract Climate forecast skills are evaluated for surface temperature time series at grid points of a millennium control simulation from a state-of-the-art global circulation model [ECHAM5–Max Planck Institute Ocean Model (MPI-OM)]. First, climate predictability is diagnosed in terms of potentially predictable variance fractions and the fluctuation power-law exponent (using detrended fluctuation analysis). Long-term memory (LTM) with a fluctuation exponent (or Hurst exponent) close to 0.9 occurs mainly in high-latitude oceans, which are also characterized by high potential predictability. Next, explicit prediction experiments for various time steps are conducted on a gridpoint basis using an autocorrelation predictor. In regions with LTM, prediction skills are beyond that expected from red noise persistence—exceptions occur in some areas in the southern oceans and over the Northern Hemisphere continents. Extending the predictability analysis to the fully forced simulation shows a large improvement in prediction skills.

scholarly journals Fractal Analysis of the Long-Term Memory in Precipitation over Bénin (West Africa)

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Medard Noukpo Agbazo ◽  
Gabin Koto N’Gobi ◽  
Eric Alamou ◽  
Basile Kounouhewa ◽  
Abel Afouda
Keyword(s):  
Transition Period ◽  
Fractal Theory ◽  
Long Term Memory ◽  
Fluctuation Analysis ◽  
Spatial Average ◽  
Term Memory ◽  
Fractal Approach ◽  
Memory Characteristic ◽  
Geographical Position

This study analyzed the long-term memory (LTM) in precipitation over Bénin synoptic stations from 1951 to 2010 using the detrended fluctuation analysis (DFA) method. Results reveal the existence of positive long-term memory characteristic in rainfall field. DFA exponent values are different regarding the concerned synoptic stations, reflecting the effect of geographical position and climate on the LTM. These values were related to the type of climate. The best DFA1-4 method depends on the geographical position of the studied station. However, DFA2 is generally the best in terms of spatial average from DFA1 to DFA4. In Bénin synoptic stations, except the Parakou station, the long-term temporal correlations are systematically the source of multifractality in rainfall. Except Natitingou, the strength of long-term memory characteristic decreases each twenty years in the study period. Considering the fractal approach, our results show that the subperiod 1991–2010 is not really a transition period as shown before. Thus, the drought is prolonging until 2010. So, fractal theory reveals more Bénin climatic characteristics.

FRACTAL DETRENDED FLUCTUATION ANALYSIS OF CHINESE ENERGY MARKETS

2010 ◽  
Vol 20 (11) ◽  
pp. 3753-3768 ◽  
Author(s):  
JUNHUAN ZHANG ◽  
JUN WANG
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Composite Index ◽  
Long Term Memory ◽  
Fluctuation Analysis ◽  
Chinese Stock Market ◽  
Long Range Correlations ◽  
Persistence Properties ◽  
Nasdaq Composite Index ◽  
Detrended Fluctuation

In this paper, we analyze and compare long-range power-law correlations of returns, absolute returns, squared returns, cubed returns and square waved returns for sixteen individual stocks from the block of energy sources of Chinese stock market and five stock indices (Shanghai Composite Index, Shenzhen Component Index, Dow Jones Industrial Average index, Nasdaq Composite Index, the Standard and Poor's 500 Index) by using a detrended fluctuation analysis approach. The empirical evidence suggests that Shanghai Composite Index is very close to Shenzhen Component Index and Nasdaq, DJIA is very close to S&P 500 in all cases. And the exponent trends of the returns are close to that of square waved returns. Also, five indices deviate from other sixteen individual energy stocks in all cases except square waved returns. Further, there are long-range correlations and persistence in volatility series of absolute returns and squared returns. Moreover, we investigate the long-term memory of these returns by applying Lo's modified rescaled range statistic. We find that the China energy market exhibits fractal and persistence properties.

scholarly journals Generalized Structure Functions and Multifractal Detrended Fluctuation Analysis Applied to Vegetation Index Time Series: An Arid Rangeland Study

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 576
Author(s):  
Ernesto Sanz ◽  
Antonio Saa-Requejo ◽  
Carlos H. Díaz-Ambrona ◽  
Margarita Ruiz-Ramos ◽  
Alfredo Rodríguez ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Vegetation Index ◽  
Spatial Diversity ◽  
Fluctuation Analysis ◽  
Term Memory ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Fractal Analyses ◽  
Detrended Fluctuation

Estimates suggest that more than 70% of the world’s rangelands are degraded. The Normalized Difference Vegetation Index (NDVI) is commonly used by ecologists and agriculturalists to monitor vegetation and contribute to more sustainable rangeland management. This paper aims to explore the scaling character of NDVI and NDVI anomaly (NDVIa) time series by applying three fractal analyses: generalized structure function (GSF), multifractal detrended fluctuation analysis (MF-DFA), and Hurst index (HI). The study was conducted in four study areas in Southeastern Spain. Results suggest a multifractal character influenced by different land uses and spatial diversity. MF-DFA indicated an antipersistent character in study areas, while GSF and HI results indicated a persistent character. Different behaviors of generalized Hurst and scaling exponents were found between herbaceous and tree dominated areas. MF-DFA and surrogate and shuffle series allow us to study multifractal sources, reflecting the importance of long-range correlations in these areas. Two types of long-range correlation appear to be in place due to short-term memory reflecting seasonality and longer-term memory based on a time scale of a year or longer. The comparison of these series also provides us with a differentiating profile to distinguish among our four study areas that can improve land use and risk management in arid rangelands.

scholarly journals Evolution of High-Viscosity Gas–Liquid Flows as Viewed Through a Detrended Fluctuation Characterization

Processes ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 822 ◽  
Author(s):  
J. Hernández ◽  
D. F. Galaviz ◽  
L. Torres ◽  
A. Palacio-Pérez ◽  
A. Rodríguez-Valdés ◽  
...  
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Ad Hoc ◽  
Flow Line ◽  
High Viscosity ◽  
Intermittent Flow ◽  
Fluctuation Analysis ◽  
Range Correlation ◽  
Liquid Flows ◽  
Detrended Fluctuation

We characterize the long-term development of high-viscosity gas–liquid intermittent flows by means of a detrended fluctuation analysis (DFA). To this end, the pressures measured at different locations along an ad hoc experimental flow line are compared. We then analyze the relevant time-series to determine the evolution of the various kinds of intermittent flow patterns associated with the mixtures under consideration. Although no pattern transitions are observed in the presence of high-viscosity mixtures, we show that the dynamical attributes of each kind of intermittence evolves from one point to another within the transport system. The analysis indicates that the loss of a long-range correlation between the pressure responses are due to the discharge processes.

scholarly journals INVESTIGATION OF HEART RATE VARIABILITY BY STATISTICAL METHODS AND DETRENDED FLUCTUATION ANALYSIS

2019 ◽  
Vol 7 ◽  
Author(s):  
Galya Nikolova Georgieva-Tsaneva
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Statistical Methods ◽  
Detrended Fluctuation Analysis ◽  
Age Groups ◽  
Research Problem ◽  
Fluctuation Analysis ◽  
Short Term ◽  
Detrended Fluctuation

The physiological signals that are recorded from different parts of the human body have a non-stationary nature and the tracking of their dynamics is an interesting research problem. This report examines Heart Rate Variability through the use of statistical methods of analysis that are traditionally used to study the functionality of the heart and via Detrended Fluctuation Analysis. The use of the technique of Detrended Fluctuation Analysis allows the investigation of short-term and long-term correlations in non-stationary Heart Rate Variability series. A study has been made of the changes in the functioning of the human heart, depending on the age. The study encompasses healthy individuals in three different age groups. The analysis of the obtained results shows a change in the correlated behavior of the investigated signals with an increase in age.

Sign in / Sign up

Export Citation Format

Share Document