A Study of Wavelet Analysis and Data Extraction from Second-Order Self-Similar Time Series
Joint Authors
Torres Román, Deni
Toral Cruz, Homero
Estrada Vargas, Leopoldo
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-18
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
Statistical analysis and synthesis of self-similar discrete time signals are presented.
The analysis equation is formally defined through a special family of basis functions of which the simplest case matches the Haar wavelet.
The original discrete time series is synthesized without loss by a linear combination of the basis functions after some scaling, displacement, and phase shift.
The decomposition is then used to synthesize a new second-order self-similar signal with a different Hurst index than the original.
The components are also used to describe the behavior of the estimated mean and variance of self-similar discrete time series.
It is shown that the sample mean, although it is unbiased, provides less information about the process mean as its Hurst index is higher.
It is also demonstrated that the classical variance estimator is biased and that the widely accepted aggregated variance-based estimator of the Hurst index results biased not due to its nature (which is being unbiased and has minimal variance) but to flaws in its implementation.
Using the proposed decomposition, the correct estimation of the Variance Plot is described, as well as its close association with the popular Logscale Diagram.
American Psychological Association (APA)
Estrada Vargas, Leopoldo& Torres Román, Deni& Toral Cruz, Homero. 2013. A Study of Wavelet Analysis and Data Extraction from Second-Order Self-Similar Time Series. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-1008448
Modern Language Association (MLA)
Estrada Vargas, Leopoldo…[et al.]. A Study of Wavelet Analysis and Data Extraction from Second-Order Self-Similar Time Series. Mathematical Problems in Engineering No. 2013 (2013), pp.1-14.
https://search.emarefa.net/detail/BIM-1008448
American Medical Association (AMA)
Estrada Vargas, Leopoldo& Torres Román, Deni& Toral Cruz, Homero. A Study of Wavelet Analysis and Data Extraction from Second-Order Self-Similar Time Series. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-14.
https://search.emarefa.net/detail/BIM-1008448
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1008448