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.


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.


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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.
Brouste, Alexandre, Jacques Istas, and Sophie Lambert-Lacroix. 2016. “Conditional Fractional Gaussian Fields with the Package FieldSim.” R JOURNAL 8 (1): 38–47. http://perso.univ-lemans.fr/~abrouste/work/BIL15.pdf.
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Greaves-Tunnell, Alexander, and Zaid Harchaoui. 2019. “A Statistical Investigation of Long Memory in Language and Music.” arXiv:1904.03834 [cs, Eess, Stat], June. http://arxiv.org/abs/1904.03834.
Hurvich, Clifford M. 2002. “Multistep Forecasting of Long Memory Series Using Fractional Exponential Models.” International Journal of Forecasting, Forecasting Long Memory Processes, 18 (2): 167–79. https://doi.org/10.1016/S0169-2070(01)00151-0.
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Lahiri, S N. 1993. “On the Moving Block Bootstrap Under Long Range Dependence.” Statistics & Probability Letters 18 (5): 405–13. https://doi.org/10.1016/0167-7152(93)90035-H.
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McCauley, Joseph L. 2008. “Time Vs. Ensemble Averages for Nonstationary Time Series.” Physica A: Statistical Mechanics and Its Applications 387 (22): 5518–22. https://doi.org/10.1016/j.physa.2008.05.057.
McLeod, A. Ian. 1998. “Hyperbolic Decay Time Series.” Journal of Time Series Analysis 19 (4): 473–83. https://doi.org/10.1111/1467-9892.00104.
Papavasiliou, Anastasia, and Kasia B. Taylor. 2016. “Approximate Likelihood Construction for Rough Differential Equations.” arXiv:1612.02536 [math, Stat], December. http://arxiv.org/abs/1612.02536.
Pipiras, Vladas, and Murad S. Taqqu. 2017. Long-Range Dependence and Self-Similarity. Cambridge Series in Statistical and Probabilistic Mathematics 45. Cambridge, United Kingdom ; New York, NY, USA: Cambridge University Press.
Saichev, A. I., and D. Sornette. 2010. “Generation-by-Generation Dissection of the Response Function in Long Memory Epidemic Processes.” The European Physical Journal B 75 (3): 343–55. https://doi.org/10.1140/epjb/e2010-00121-7.
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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