Mandelbrot's stochastic time series models

Watkins, N. W. ORCID: 0000-0003-4484-6588 (2019) Mandelbrot's stochastic time series models. Earth and Space Science, 6 (11). 2044 - 2056. ISSN 2333-5084

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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:	Article
Official URL:	https://agupubs.onlinelibrary.wiley.com/journal/23...
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:	12 Dec 2024 01:58
URI:	http://eprints.lse.ac.uk/id/eprint/102474

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