Long memory time series

November 13, 2011 — May 28, 2020

model selection
regression
self similar
signal processing
statistics
stochastic processes
time series
Figure 1

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 to be fractal models, so note power laws, \(1/f\) noise, fractional Brownian motion, etc. Link to branching processes.

1 References

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———. 1994. Statistics for Long-Memory Processes.
———. 2010. “Long-Range Dependence.” 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.
Chen. 2011. “Zipf’s Law, 1/f Noise, and Fractal Hierarchy.” Chaos, Solitons & Fractals.
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