# Long memory 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 here, 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.

## References

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———. 1994. Statistics for Long-Memory Processes. CRC Press.
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Beran, Jan, and Norma Terrin. 1996. “Testing for a Change of the Long-Memory Parameter.” Biometrika 83 (3): 627–38. https://doi.org/10.1093/biomet/83.3.627.
Berkes, István, Lajos Horváth, Piotr Kokoszka, and Qi-Man Shao. 2006. “On Discriminating Between Long-Range Dependence and Changes in Mean.” The Annals of Statistics 34 (3): 1140–65. https://doi.org/10.1214/009053606000000254.
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Schmitt, Francois G., and Yongxiang Huang. 2016. Stochastic Analysis of Scaling Time Series: From Turbulence Theory to Applications. Cambridge: Cambridge University Press.

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