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Mandelbrot's stochastic time series models

Watkins, N. W. (2019) Mandelbrot's stochastic time series models. Earth and Space Science, 6 (11). 2044 - 2056. ISSN 2333-5084

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Identification Number: 10.1029/2019EA000598


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: Article
Official URL:
Additional Information: © 2019 The Author
Divisions: Centre for Analysis of Time Series
Subjects: Q Science > QA Mathematics
G Geography. Anthropology. Recreation > GA Mathematical geography. Cartography
Q Science > QC Physics
Date Deposited: 11 Nov 2019 14:42
Last Modified: 20 Oct 2021 02:45

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