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2017 | OriginalPaper | Buchkapitel

Mandelbrot’s 1/f Fractional Renewal Models of 1963–67: The Non-ergodic Missing Link Between Change Points and Long Range Dependence

verfasst von : Nicholas Wynn Watkins

Erschienen in: Advances in Time Series Analysis and Forecasting

Verlag: Springer International Publishing

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Abstract

The problem of 1/f noise was identified by physicists about a century ago, while the puzzle posed by Hurst’s eponymous effect, originally identified by statisticians, hydrologists and time series analysts, is over 60 years old. Because these communities so often frame the problems in Fourier spectral language, the most famous solutions have tended to be the stationary ergodic long range dependent (LRD) models such as Mandelbrot’s fractional Gaussian noise. In view of the increasing importance to physics of non-ergodic fractional renewal processes (FRP), I present the first results of my research into the history of Mandelbrot’s very little known work on the FRP in 1963–67. I discuss the differences between the Hurst effect, 1/f noise and LRD, concepts which are often treated as equivalent, and finally speculate about how the lack of awareness of his FRP papers in the physics and statistics communities may have affected the development of complexity science.

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Titel: Mandelbrot’s 1/f Fractional Renewal Models of 1963–67: The Non-ergodic Missing Link Between Change Points and Long Range Dependence
verfasst von: Nicholas Wynn Watkins
Verlag: Springer International Publishing
Buch: Advances in Time Series Analysis and Forecasting
Print ISBN: 978-3-319-55788-5

Electronic ISBN: 978-3-319-55789-2

Copyright-Jahr: 2017
DOI: https://doi.org/10.1007/978-3-319-55789-2_14

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