scholarly journals Probabilistic analysis of recurrence plots generated by fractional Gaussian noise

2018 ◽  
Vol 28 (8) ◽  
pp. 085721 ◽  
Author(s):  
Sofiane Ramdani ◽  
Frédéric Bouchara ◽  
Annick Lesne
Keyword(s):  
Probabilistic Analysis ◽  
Gaussian Noise ◽  
Fractional Gaussian Noise ◽  
Recurrence Plots

scholarly journals Generalized Wavelet Fisher’s Information of1/fαSignals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Julio Ramírez-Pacheco ◽  
Homero Toral-Cruz ◽  
Luis Rizo-Domínguez ◽  
Joaquin Cortez-Gonzalez
Keyword(s):  
Fisher Information ◽  
Gaussian Noise ◽  
Structural Breaks ◽  
Wavelet Domain ◽  
Fractional Gaussian Noise ◽  
Domain Definition ◽  
Potential Applications ◽  
Definition Of ◽  
The Time Domain ◽  
Fisher's Information

This paper defines the generalized wavelet Fisher information of parameterq. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for1/fαsignals are determined and a detailed discussion of their properties, characteristics and their relationship with waveletq-Fisher information are given. Information planes of1/fsignals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary1/fsignals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of theF-statistic.

Permutation entropy of fractional Brownian motion and fractional Gaussian noise

2008 ◽  
Vol 372 (27-28) ◽  
pp. 4768-4774 ◽  
Author(s):  
L. Zunino ◽  
D.G. Pérez ◽  
M.T. Martín ◽  
M. Garavaglia ◽  
A. Plastino ◽  
...  
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Gaussian Noise ◽  
Permutation Entropy ◽  
Fractional Gaussian Noise

scholarly journals Variance Bound of ACF Estimation of One Block of fGn with LRD

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Long Range ◽  
Autocorrelation Function ◽  
Gaussian Noise ◽  
Block Size ◽  
Long Range Dependence ◽  
Hurst Parameter ◽  
Sample Length ◽  
Fractional Gaussian Noise ◽  
Variance Bound ◽  
Data Points

This paper discusses the estimation of autocorrelation function (ACF) of fractional Gaussian noise (fGn) with long-range dependence (LRD). A variance bound of ACF estimation of one block of fGn with LRD for a given value of the Hurst parameter (H) is given. The present bound provides a guideline to require the block size to guarantee that the variance of ACF estimation of one block of fGn with LRD for a givenHvalue does not exceed the predetermined variance bound regardless of the start point of the block. In addition, the present result implies that the error of ACF estimation of a block of fGn with LRD depends only on the number of data points within the sample and not on the actual sample length in time. For a given block size, the error is found to be larger for fGn with stronger LRD than that with weaker LRD.

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