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 |
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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: | 29 Nov 2024 19:27 |
URI: | http://eprints.lse.ac.uk/id/eprint/102474 |
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