Stationarity in stochastic processes

Change-points, trends and transients



Non-stationary dynamics turn out to be important in practice.

Notes on detecting non-stationarity in stochastic processes/random fields.

Related: ensuring stability. If we have a system with stable dynamics and keep the distribution of the inputs the same, then it will end up stationary.

Shay Palachy, Detecting stationarity in time series data

Change point methods

Nonparametric methods

References

Adams, Ryan Prescott, and David J. C. MacKay. 2007. β€œBayesian Online Changepoint Detection.” arXiv:0710.3742 [Stat], October.
Borgnat, Pierre, Patrick Flandrin, Paul Honeine, CΓ©dric Richard, and Jun Xiao. 2010. β€œTesting Stationarity With Surrogates: A Time-Frequency Approach.” IEEE Transactions on Signal Processing 58 (7): 3459–70.
Delft, Anne van, Vaidotas Characiejus, and Holger Dette. 2021. β€œA Nonparametric Test for Stationarity in Functional Time Series.” Statistica Sinica.
Delft, Anne van, and Michael Eichler. 2018. β€œLocally Stationary Functional Time Series.” Electronic Journal of Statistics 12 (1).
Dette, Holger, Philip Preuß, and Mathias Vetter. 2011. β€œA Measure of Stationarity in Locally Stationary Processes With Applications to Testing.” Journal of the American Statistical Association 106 (495): 1113–24.
Hegger, Rainer, Holger Kantz, Lorenzo Matassini, and Thomas Schreiber. 2000. β€œCoping with Nonstationarity by Overembedding.” Phys. Rev.Β Lett. 84 (18): 4092–95.
Livan, Giacomo, Jun-ichi Inoue, and Enrico Scalas. 2012. β€œOn the Non-Stationarity of Financial Time Series: Impact on Optimal Portfolio Selection.” Journal of Statistical Mechanics: Theory and Experiment 2012 (07): P07025.
Paparoditis, Efstathios. 2010. β€œValidating Stationarity Assumptions in Time Series Analysis by Rolling Local Periodograms.” Journal of the American Statistical Association 105 (490): 839–51.
Preuß, Philip, Mathias Vetter, and Holger Dette. 2013. β€œA Test for Stationarity Based on Empirical Processes.” Bernoulli 19 (5B): 2715–49.
SaatΓ§i, Yunus, Ryan Turner, and Carl Edward Rasmussen. 2010. β€œGaussian Process Change Point Models.” In Proceedings of the 27th International Conference on International Conference on Machine Learning, 927–34. ICML’10. Madison, WI, USA: Omnipress.
Shalizi, Cosma Rohilla, Abigail Z Jacobs, and Aaron Clauset. n.d. β€œAdapting to Non-Stationarity with Growing Expert Ensembles.”
Shinohara, Shuji, Nobuhito Manome, Kouta Suzuki, Ung-il Chung, Tatsuji Takahashi, Hiroshi Okamoto, Yukio Pegio Gunji, Yoshihiro Nakajima, and Shunji Mitsuyoshi. 2020. β€œA New Method of Bayesian Causal Inference in Non-Stationary Environments.” PLOS ONE 15 (5): e0233559.
Thorisson, Hermann. 2000. Coupling, Stationarity, and Regeneration. Springer New York.
Vogt, Michael, and Holger Dette. 2015. β€œDetecting Gradual Changes in Locally Stationary Processes.” The Annals of Statistics 43 (2): 713–40.
Von Sachs, Rainer, and Michael H. Neumann. 2000. β€œA Wavelet-Based Test for Stationarity.” Journal of Time Series Analysis 21 (5): 597–613.

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