On the Predictability of Long‐Range Dependent Series

Li, Ming; Li, Jiayue

doi:10.1155/2010/397454

Cited by 36 publications

(9 citation statements)

References 77 publications

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“…In the latter case, special techniques have to be considered [75–78]. For instance, weighting prediction error may be a technique necessarily to be taken into account, which is suggested in the domain of generalized functions over the Schwartz distributions [79]. …”

Section: Discussionmentioning

confidence: 99%

Heavy-Tailed Prediction Error: A Difficulty in Predicting Biomedical Signals of1/fNoise Type

Zhao

Chen

2012

Computational and Mathematical Methods in Medicine

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A fractal signal x(t) in biomedical engineering may be characterized by 1/f noise, that is, the power spectrum density (PSD) divergences at f = 0. According the Taqqu's law, 1/f noise has the properties of long-range dependence and heavy-tailed probability density function (PDF). The contribution of this paper is to exhibit that the prediction error of a biomedical signal of 1/f noise type is long-range dependent (LRD). Thus, it is heavy-tailed and of 1/f noise. Consequently, the variance of the prediction error is usually large or may not exist, making predicting biomedical signals of 1/f noise type difficult.

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Section: Discussionmentioning

confidence: 99%

Heavy-Tailed Prediction Error: A Difficulty in Predicting Biomedical Signals of1/fNoise Type

Zhao

Chen

2012

Computational and Mathematical Methods in Medicine

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“…Let X " px t : t " 1, 2, 3...q be a stochastic process with the ACF r xx pτq " Erxptqxpt`τqs, then X is called SRD series if r xx pτq is integrable [16,29], that is ş 8 0 r xx pτqdτ ă 8, on the other side, X is LRD if r xx pτq is nonintegrable, that is ş 8 0 r xx pτqdτ " 8. Moreover, the autocorrelation function follows asymptotically:…”

Section: Theory Of Long Range Dependencementioning

confidence: 99%

Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series

Liang

Yang

et al. 2016

Entropy

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According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD) is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and the optimal embedding dimension and saturated correlation dimension are calculated via the Grassberger-Procaccia (G-P) method, respectively, so that the chaotic characteristics of vibration intensity time series can be jointly determined by the largest Lyapunov exponent and phase plane trajectory of vibration intensity time series, meanwhile, the largest Lyapunov exponent is calculated by the Wolf method and phase plane trajectory is illustrated using Duffing-Holmes Oscillator (DHO). The Hurst exponent and long range dependence prediction method are proposed to verify the typical fractional order features and improve the prediction accuracy of bearing vibration intensity time series, respectively. Experience shows that the vibration intensity time series have chaotic properties and the LRD prediction method is better than the other prediction methods (largest Lyapunov, auto regressive moving average (ARMA) and BP neural network (BPNN) model) in prediction accuracy and prediction performance, which provides a new approach for running tendency predictions for rotating machinery and provide some guidance value to the engineering practice.

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“…where denotes averaging over the ensemble, and H is the Hurst index. The scaling behavior of the different traces, V H x , is characterized by a particular H which relate the typical change in Δz x , where z x V H x , is the trace of the fBm, and the change in the spatial coordinate Δx by the simple scaling law 36,39,40 :…”

Section: Brownian Surfaces and Random Fractalsmentioning

confidence: 99%

Recent Advancements in Fractal Geometric‐Based Nonlinear Time Series Solutions to the Micro‐Quasistatic Thermoviscoelastic Creep for Rough Surfaces in Contact

Abuzeid

Al‐Rabadi

Alkhaldi

2011

Mathematical Problems in Engineering

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To understand the tripological contact phenomena, both mathematical and experimental models are needed. In this work, fractal mathematical models are used to model the experimental results obtained from literature. Fractal geometry, using a deterministic Cantor structure, is used to model the surface topography, where recent advancements in thermoviscoelastic creep contact of rough surfaces are introduced. Various viscoelastic idealizations are used to model the surface materials, for example, Maxwell, Kelvin-Voigt, Standard Linear Solid and Jeffrey media. Such media are modelled as arrangements of elastic springs and viscous dashpots in parallel and/or in series. Asymptotic power laws, through hypergeometric series, were used to express the surface creep as a function of remote forces, body temperatures and time. The introduced models are valid only when the creep approach of the contact surfaces is in the order of the size of the surface roughness. The obtained results using such models, which admit closed-form solutions, are displayed graphically for selected values of the systems' parameters; the fractal surface roughness and various material properties. Results obtained showed good agreement with published experimental results, where the utilized methodology can be further extended to the utilization for the contact of surfaces within micro- and nano-electronic devices, circuits and systems.

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On the Predictability of Long‐Range Dependent Series

Cited by 36 publications

References 77 publications

Heavy-Tailed Prediction Error: A Difficulty in Predicting Biomedical Signals of1/fNoise Type

Heavy-Tailed Prediction Error: A Difficulty in Predicting Biomedical Signals of1/fNoise Type

Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series

Recent Advancements in Fractal Geometric‐Based Nonlinear Time Series Solutions to the Micro‐Quasistatic Thermoviscoelastic Creep for Rough Surfaces in Contact

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