# Long memory time series

November 14, 2011 — May 28, 2020

model selection

regression

self similar

signal processing

statistics

stochastic processes

time series

Hurst exponents, non-stationarity etc. I used to do a lot of work in this area, but have not now for so long that I no longer claim any authority.

TBD.

Many interesting things, but for now, note that many natural generic models of long-memory in time series turn out ot be fractal models, so note power laws, \(1/f\) noise, fractional brownian motion etc. Link to branching processes.

## 1 References

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*Statistics for Long-Memory Processes*.
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*Wiley Interdisciplinary Reviews: Computational Statistics*.
Beran, and Terrin. 1996. “Testing for a Change of the Long-Memory Parameter.”

*Biometrika*.
Berkes, Horváth, Kokoszka, et al. 2006. “On Discriminating Between Long-Range Dependence and Changes in Mean.”

*The Annals of Statistics*.
Brouste, Istas, and Lambert-Lacroix. 2016. “Conditional Fractional Gaussian Fields with the Package FieldSim.”

*R JOURNAL*.
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*Bernoulli*.
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*MSc Theses, University of Twente, Amsterdam, The Netherlands*.
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*Journal of Time Series Analysis*.
Greaves-Tunnell, and Harchaoui. 2019. “A Statistical Investigation of Long Memory in Language and Music.”

*arXiv:1904.03834 [Cs, Eess, Stat]*.
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*International Journal of Forecasting*, Forecasting Long Memory Processes,.
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*Journal of Applied Probability*.
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*Statistics & Probability Letters*.
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*Multifractals and 1/ƒ Noise: Wild Self-Affinity in Physics (1963–1976)*.
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*arXiv:1612.02536 [Math, Stat]*.
Pipiras, and Taqqu. 2017.

*Long-Range Dependence and Self-Similarity*. Cambridge Series in Statistical and Probabilistic Mathematics 45.
Saichev, and Sornette. 2010. “Generation-by-Generation Dissection of the Response Function in Long Memory Epidemic Processes.”

*The European Physical Journal B*.
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*Stochastic Analysis of Scaling Time Series: From Turbulence Theory to Applications*.