scholarly journals DETRENDED FLUCTUATION ANALYSIS OF AUTOREGRESSIVE PROCESSES

2007 ◽  
Vol 07 (03) ◽  
pp. L249-L255 ◽  
Author(s):  
VASILE V. MORARIU ◽  
LUIZA BUIMAGA-IARINCA ◽  
CĂLIN VAMOŞ ◽  
ŞTEFAN M. ŞOLTUZ
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Short Range ◽  
Interaction Constant ◽  
Fluctuation Analysis ◽  
Autoregressive Processes ◽  
Long Range Correlations ◽  
Correlation Exponent ◽  
The Relationship ◽  
Detrended Fluctuation

Autoregressive processes (AR) have typical short-range memory. Detrended Fluctuation Analysis (DFA) was basically designed to reveal long-range correlations in non stationary processes. However DFA can also be regarded as a suitable method to investigate both long-range and short-range correlations in non stationary and stationary systems. Applying DFA to AR processes can help understanding the non-uniform correlation structure of such processes. We systematically investigated a first order autoregressive model AR(1) by DFA and established the relationship between the interaction constant of AR(1) and the DFA correlation exponent. The higher the interaction constant the higher is the short-range correlation exponent. They are exponentially related. The investigation was extended to AR(2) processes. The presence of an interaction between distant terms with characteristic time constant in the series, in addition to a near by interaction will increase the correlation exponent and the range of correlation while the effect of a distant negative interaction will significantly decrease the range of interaction, only. This analysis demonstrate the possibility to identify an AR(1) model in an unknown DFA plot or to distinguish between AR(1) and AR(2) models.

scholarly journals Early Warning Signals for Bearing Failure Using Detrended Fluctuation Analysis

2020 ◽  
Vol 10 (23) ◽  
pp. 8489
Author(s):  
Laith Shalalfeh ◽  
Ashraf AlShalalfeh
Keyword(s):  
Long Range ◽  
Early Warning ◽  
Detrended Fluctuation Analysis ◽  
Short Range ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Bearing Failure ◽  
Kendall’S Tau ◽  
Vibration Data ◽  
Detrended Fluctuation

Prognostic techniques play a critical role in predicting upcoming faults and failures in machinery or a system by monitoring any deviation in the operation. This paper presents a novel method to analyze multidimensional sensory data and use its characteristics in bearing health prognostics. Firstly, detrended fluctuation analysis (DFA) is exploited to evaluate the long-range correlations in ball bearing vibration data. The results reveal the existence of the crossover phenomenon in vibration data with two scaling exponents at the short-range and long-range scales. Among several data sets, applying the DFA method to vibration signals shows a consistent increase in the short-range scaling exponent toward bearing failure. Finally, Kendall’s tau is used as a ranking coefficient to quantify the trend in the scaling exponent. It was found that the Kendall’s tau coefficient of the vibration scaling exponent could provide an early warning signal (EWS) for bearing failure.

scholarly journals Scaling behaviour of the global tropopause

2009 ◽  
Vol 9 (2) ◽  
pp. 677-683 ◽  
Author(s):  
C. Varotsos ◽  
M. Efstathiou ◽  
C. Tzanis
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Sea Surface ◽  
Fluctuation Analysis ◽  
Tropopause Height ◽  
Time Intervals ◽  
Long Range Correlations ◽  
Scaling Behaviour ◽  
Detrended Fluctuation ◽  
Global Mean

Abstract. Detrended fluctuation analysis is applied to the time series of the global tropopause height derived from the 1980–2004 daily radiosonde data, in order to detect long-range correlations in its time evolution. Global tropopause height fluctuations in small time-intervals are found to be positively correlated to those in larger time intervals in a power-law fashion. The exponent of this dependence is larger in the tropics than in the middle and high latitudes in both hemispheres. Greater persistence is observed in the tropopause of the Northern than in the Southern Hemisphere. A plausible physical explanation of the fact that long-range correlations in tropopause variability decreases with increasing latitude is that the column ozone fluctuations (that are closely related with the tropopause ones) exhibit long range correlations, which are larger in tropics than in the middle and high latitudes at long time scales. This finding for the tropopause height variability should reduce the existing uncertainties in assessing the climatic characteristics. More specifically the reliably modelled values of a climatic variable (i.e. past and future simulations) must exhibit the same scaling behaviour with that possibly existing in the real observations of the variable under consideration. An effort has been made to this end by applying the detrended fluctuation analysis to the global mean monthly land and sea surface temperature anomalies during the period January 1850–August 2008. The result obtained supports the findings presented above, notably: the correlations between the fluctuations in the global mean monthly land and sea surface temperature display scaling behaviour which must characterizes any projection.

scholarly journals IMPACT OF TANDEM REPEATS ON THE SCALING OF NUCLEOTIDE SEQUENCES

2006 ◽  
Vol 16 (10) ◽  
pp. 3103-3108
Author(s):  
RADHAKRISHNAN NAGARAJAN ◽  
MEENAKSHI UPRETI
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Tandem Repeats ◽  
Nucleotide Sequences ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Long Range Correlations ◽  
Reliable Estimation ◽  
Detrended Fluctuation

Techniques such as detrended fluctuation analysis (DFA) and its extensions have been widely used to determine the nature of scaling in nucleotide sequences. In this brief communication we show that tandem repeats which are ubiquitous in nucleotide sequences can prevent reliable estimation of possible long-range correlations. Therefore, it is important to investigate the presence of tandem repeats prior to scaling exponent estimation.

scholarly journals Fractal Analysis of Deep Ocean Current Speed Time Series

2017 ◽  
Vol 34 (4) ◽  
pp. 817-827 ◽  
Author(s):  
Laura Cabrera-Brito ◽  
German Rodriguez ◽  
Luis García-Weil ◽  
Mercedes Pacheco ◽  
Esther Perez ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Single Point ◽  
Deep Ocean ◽  
Current Speed ◽  
Ocean Current ◽  
Fluctuation Analysis ◽  
Long Range Correlations ◽  
Detrended Fluctuation

AbstractFractal properties of deep ocean current speed time series, measured at a single-point mooring on the Madeira Abyssal Plain at 1000- and 3000-m depth, are explored over the range between one week and 5 years, by using the detrended fluctuation analysis and multifractal detrended fluctuation analysis methodologies. The detrended fluctuation analysis reveals the existence of two subranges with different scaling behaviors. Long-range temporal correlations following a power law are found in the time-scale range between approximately 50 days and 5 years, while a Brownian motion–type behavior is observed for shorter time scales. The multifractal analysis approach underlines a multifractal structure whose intensity decreases with depth. The analysis of the shuffled and surrogate versions of the original time series shows that multifractality is mainly due to long-range correlations, although there is a weak nonlinear contribution at 1000-m depth, which is confirmed by the detrended fluctuation analysis of volatility time series.

scholarly journals MINIMIZING THE EFFECT OF SINUSOIDAL TRENDS IN DETRENDED FLUCTUATION ANALYSIS

2005 ◽  
Vol 15 (05) ◽  
pp. 1767-1773 ◽  
Author(s):  
RADHAKRISHNAN NAGARAJAN ◽  
RAJESH G. KAVASSERI
Keyword(s):  
Long Range ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Long Range Correlations ◽  
Smoothing Filter ◽  
Detrended Fluctuation

The detrended fluctuation analysis (DFA) [Peng et al., 1994] and its extensions (MF-DFA) [Kantelhardt et al., 2002] have been used extensively to determine possible long-range correlations in self-affine signals. While the DFA has been claimed to be a superior technique, recent reports have indicated its susceptibility to trends in the data. In this report, a smoothing filter is proposed to minimize the effect of sinusoidal trends and distortion in the log–log plots obtained by DFA and MF-DFA techniques.

THE ORTHOGONAL V-SYSTEM DETRENDED FLUCTUATION ANALYSIS

2011 ◽  
Vol 10 (02) ◽  
pp. 189-206 ◽  
Author(s):  
AIJING LIN ◽  
PENGJIAN SHANG ◽  
HUI MA
Keyword(s):  
Long Range ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Smoothing Algorithm ◽  
Scaling Exponents ◽  
Long Range Correlations ◽  
Piecewise Function ◽  
Robust Techniques ◽  
Detrended Fluctuation

The Detrended Fluctuation Analysis (DFA) and its extensions (MF-DFA) have been proposed as robust techniques to determine possible long-range correlations in self-affine signals. However, many studies have reported the susceptibility of DFA to trends which give rise to spurious crossovers and prevent reliable estimations of the scaling exponents. Lately, several modifications of the DFA method have been reported with many different techniques for eliminating the monotonous and periodic trends. In this study, a smoothing algorithm based on the Orthogonal V-system (OVS) is proposed to minimize the effect of power-law trends, periodic trends, assembled trends and piecewise function trends. The effectiveness of the new method is demonstrated on monofractal data and multifractal data corrupted with different trends.

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