The Open UniversitySkip to content

Mandelbrot's stochastic time series models

Watkins, N. W. (2019). Mandelbrot's stochastic time series models. Earth and Space Science (Early Access).

Full text available as:
PDF (Version of Record) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (5MB) | Preview
DOI (Digital Object Identifier) Link:
Google Scholar: Look up in Google Scholar


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 Item
Copyright Holders: 2019 The Author
ISSN: 2333-5084
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Engineering and Innovation
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 68043
SWORD Depositor: Jisc Publications-Router
Depositing User: Jisc Publications-Router
Date Deposited: 11 Nov 2019 09:04
Last Modified: 12 Nov 2019 06:21
Share this page:


Altmetrics from Altmetric

Citations from Dimensions

Download history for this item

These details should be considered as only a guide to the number of downloads performed manually. Algorithmic methods have been applied in an attempt to remove automated downloads from the displayed statistics but no guarantee can be made as to the accuracy of the figures.

Actions (login may be required)

Policies | Disclaimer

© The Open University   contact the OU