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Mandelbrot's stochastic time series models
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Watkins, Nicholas W. (2019) Mandelbrot's stochastic time series models. Earth and Space Science, 6 (11). pp. 2044-2056. doi:10.1029/2019ea000598 ISSN 2333-5084.
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Official URL: https://doi.org/10.1029/2019ea000598
Abstract
I survey and illustrate the main time series models that Mandelbrot introduced into time series analysis in the 1960s and 1970s. I focus particularly on the members of the additive fractional stable family including Lévy flights and fractional Brownian motion (fBm), noting some of the less well‐known aspects of this family, such as the cases when the self‐similarity exponent H and the Hurst exponent J differ. I briefly discuss the role of multiplicative models in modeling the physics of cascades. I then recount the still little‐known story of Mandelbrot's work on fractional renewal models in the late 1960s, explaining how these differ from their more familiar fBm counterpart and form a “missing link” between fBm and the problem of random change points. I conclude by highlighting the frontier problem of damped fractional models.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||||||||||
SWORD Depositor: | Library Publications Router | ||||||||||||
Library of Congress Subject Headings (LCSH): | Time-series analysis -- Research, Mandelbrot, Benoit B., Fractal analysis, Stochastic models | ||||||||||||
Journal or Publication Title: | Earth and Space Science | ||||||||||||
Publisher: | American Geophysical Union (AGU) | ||||||||||||
ISSN: | 2333-5084 | ||||||||||||
Official Date: | November 2019 | ||||||||||||
Dates: |
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Volume: | 6 | ||||||||||||
Number: | 11 | ||||||||||||
Page Range: | pp. 2044-2056 | ||||||||||||
DOI: | 10.1029/2019ea000598 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | "This is the peer reviewed version of the following article: Watkins, N. W. ( 2019). Mandelbrot's stochastic time series models. Earth and Space Science. 6., which has been published in final form at https://doi.org/10.1029/2019EA000598. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions." | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 12 November 2019 | ||||||||||||
Date of first compliant Open Access: | 14 November 2019 | ||||||||||||
RIOXX Funder/Project Grant: |
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