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Fractal Time Series—A Tutorial Review
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-26, 26 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-12-03
Country of Publication
Egypt
No. of Pages
26
Main Subjects
Abstract EN
Fractal time series substantially differs from conventional one in its statistic properties.
For instance, it may have a heavy-tailed probability distribution function (PDF), a slowly decayed autocorrelation function (ACF), and a power spectrum function (PSD) of 1/f type.
It may have the statistical dependence, either long-range dependence (LRD) or short-range dependence (SRD), and global or local self-similarity.
This article will give a tutorial review about those concepts.
Note that a conventional time series can be regarded as the solution to a differential equation of integer order with the excitation of white noise in mathematics.
In engineering, such as mechanical engineering or electronics engineering, engineers may usually consider it as the output or response of a differential system or filter of integer order under the excitation of white noise.
In this paper, a fractal time series is taken as the solution to a differential equation of fractional order or a response of a fractional system or a fractional filter driven with a white noise in the domain of stochastic processes.
American Psychological Association (APA)
Li, Ming. 2009. Fractal Time Series—A Tutorial Review. Mathematical Problems in Engineering،Vol. 2010, no. 2010, pp.1-26.
https://search.emarefa.net/detail/BIM-450366
Modern Language Association (MLA)
Li, Ming. Fractal Time Series—A Tutorial Review. Mathematical Problems in Engineering No. 2010 (2010), pp.1-26.
https://search.emarefa.net/detail/BIM-450366
American Medical Association (AMA)
Li, Ming. Fractal Time Series—A Tutorial Review. Mathematical Problems in Engineering. 2009. Vol. 2010, no. 2010, pp.1-26.
https://search.emarefa.net/detail/BIM-450366
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-450366