Impact of Scaling Range on the Effectiveness of Detrending Methods

Grech, Dariusz; Mazur, Zygmunt

doi:10.12693/aphyspola.127.a-59

Cited by 12 publications

(16 citation statements)

References 26 publications

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“…As a way to characterize nonstationary data with trend, the detrended fluctuation analysis (DFA) [9,10], and the detrending moving average (DMA) analysis [11][12][13][14] have been proposed to quantify long-range autocorrelations, multifractal features [15][16][17][18][19], cross-correlation [20,21] and higher dimensional fractals [22][23][24][25] either in the time or in the space domain. According to the DFA, the time series is first divided in boxes of equal lengths, then trends are estimated as least-squares polynomial fitting of different orders m in each non-overlapping and equally spaced box of length n. The DMA algorithm has been proposed as an alternative technique to quantify long-range correlations.…”

Section: Introductionmentioning

confidence: 99%

Detrending moving average algorithm: Frequency response and scaling performances

Carbone

Kiyono

2016

Phys. Rev. E

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The Detrending Moving Average (DMA) algorithm has been widely used in its several variants for characterizing long-range correlations of random signals and sets (one-dimensional sequences or highdimensional arrays) either over time or space. In this paper, mainly based on analytical arguments, the scaling performances of the centered DMA, including higher-order ones, are investigated by means of a continuous time approximation and a frequency response approach. Our results are also confirmed by numerical tests. The study is carried out for higher-order DMA operating with moving average polynomials of different degree. In particular, detrending power degree, frequency response, asymptotic scaling, upper limit of the detectable scaling exponent and finite scale range behavior will be discussed.

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Section: Introductionmentioning

confidence: 99%

Detrending moving average algorithm: Frequency response and scaling performances

Carbone

Kiyono

2016

Phys. Rev. E

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“…The problem of choosing an appropriate length for scaling range has been examined in the papers. [49][50][51] The impact of scaling range on the e®ectiveness of some detranding methods (including DFA and DMA) has been investigated in the same works. The authors¯nd the actual scaling range for which the real value of correlation exponent is strictly reproduced.…”

Section: Self-similarity Analysismentioning

confidence: 99%

Measuring long-range correlations in news flow intensity time series

Sidorov

Faizliev

Balash

2017

Int. J. Mod. Phys. C

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We consider the°ow intensity of economic and¯nancial news taken from a nine-month period of 2015. This data is found to be well approximated by a persistent self-a±ne walk. It is characterized by a Hurst exponent of H > 0:6 over three orders of magnitude in time ranging from minutes to several days. In this paper, we use the Detrended Fluctuation Analysis (DFA) of order 1, Rescaled Range Analysis (R/S) and Fourier Transform Method (FTM) to examine long-range auto-correlation and self-similarity of time series of news°ow intensity. DFA method allowed us to reveal a strong scaling behavior as well as to detect a distinct crossover e®ect. On the other hand, it turns out that for the classic R/S analysis and Fourier transform techniques, the scaling regimes and/or positions of cross-overs are hard to de¯ne.

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“…Even though the method is not directly connected to the power-law decay of auto-correlations nor to the scaling of variances of the partial sums nor the diverging power spectrum, it has been frequently applied mainly due to its computational efficiency. The connection between the estimator itself and the actual long-range dependence -that the variance of integrated series of the long-range dependent process follows a power-law with respect to the length of the moving window -has been shown numerically [48,34,49].…”

Section: Detrended Moving-average Cross-correlation Analysismentioning

confidence: 99%

Finite sample properties of power-law cross-correlations estimators

Krištoufek

2015

Physica A: Statistical Mechanics and its Applications

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We study finite sample properties of estimators of power-law cross-correlations -detrended crosscorrelation analysis (DCCA), height cross-correlation analysis (HXA) and detrending movingaverage cross-correlation analysis (DMCA) -with a special focus on short-term memory bias as well as power-law coherency. Presented broad Monte Carlo simulation study focuses on different time series lengths, specific methods' parameter setting, and memory strength. We find that each method is best suited for different time series dynamics so that there is no clear winner between the three. The method selection should be then made based on observed dynamic properties of the analyzed series.

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Impact of Scaling Range on the Effectiveness of Detrending Methods

Cited by 12 publications

References 26 publications

Detrending moving average algorithm: Frequency response and scaling performances

Detrending moving average algorithm: Frequency response and scaling performances

Measuring long-range correlations in news flow intensity time series

Finite sample properties of power-law cross-correlations estimators

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