Long memory time series
2011-11-13 — 2020-05-28
Wherein the Role of Hurst Exponents and Fractal Models Is Examined, and Links to 1/F Noise, Fractional Brownian Motion and Branching Processes Are Indicated as Generic Mechanisms for Long Memory
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 to be fractal models, so note power laws, \(1/f\) noise, fractional Brownian motion, etc. Link to branching processes.
1 References
Beran. 1992. “Statistical Methods for Data with Long-Range Dependence.” Statistical Science.
———. 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.
Csörgö, and Mielniczuk. 1999. “Random-Design Regression Under Long-Range Dependent Errors.” Bernoulli.
Dieker. 2004. “Simulation of Fractional Brownian Motion.” MSc Theses, University of Twente, Amsterdam, The Netherlands.
Doukhan, Oppenheim, and Taqqu. 2003. Theory and Applications of Long-Range Dependence.
Giraitis, and Surgailis. 1999. “Central Limit Theorem for the Empirical Process of a Linear Sequence with Long Memory.” Journal of Statistical Planning and Inference.
Granger, and Joyeux. 1980. “An Introduction to Long-Memory Time Series Models and Fractional Differencing.” 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].
Hurvich. 2002. “Multistep Forecasting of Long Memory Series Using Fractional Exponential Models.” International Journal of Forecasting, Forecasting Long Memory Processes,.
Künsch. 1986. “Discrimination Between Monotonic Trends and Long-Range Dependence.” Journal of Applied Probability.
Lahiri. 1993. “On the Moving Block Bootstrap Under Long Range Dependence.” Statistics & Probability Letters.
Mandelbrot. 1999. Multifractals and 1/ƒ Noise: Wild Self-Affinity in Physics (1963–1976).
McCauley. 2008. “Time Vs. Ensemble Averages for Nonstationary Time Series.” Physica A: Statistical Mechanics and Its Applications.
McLeod. 1998. “Hyperbolic Decay Time Series.” Journal of Time Series Analysis.
Papavasiliou, and Taylor. 2016. “Approximate Likelihood Construction for Rough Differential Equations.” 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.
Schmitt, and Huang. 2016. Stochastic Analysis of Scaling Time Series: From Turbulence Theory to Applications.