Detecting stationarity in stochastic processes
Change-points, trends and transients
November 28, 2021 — April 1, 2022
Notes on detecting non-stationarity in stochastic processes/random fields.
Related: ensuring stability in a stochastic process. 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.
1 Change point methods
See change points.
2 Nonparametric detection of changepoints
3 Spectral methods
4 References
Adams, and MacKay. 2007. “Bayesian Online Changepoint Detection.” arXiv:0710.3742 [Stat].
Aue, and van Delft. 2020. “Testing for Stationarity of Functional Time Series in the Frequency Domain.” The Annals of Statistics.
Bagchi, Characiejus, and Dette. 2017. “A Simple Test for White Noise in Functional Time Series.” arXiv:1612.04996 [Math, Stat].
Berkes, Gabrys, Horváth, et al. 2009. “Detecting Changes in the Mean of Functional Observations.” Journal of the Royal Statistical Society: Series B (Statistical Methodology).
Borgnat, Flandrin, Honeine, et al. 2010. “Testing Stationarity With Surrogates: A Time-Frequency Approach.” IEEE Transactions on Signal Processing.
Dette, Preuß, and Vetter. 2011. “A Measure of Stationarity in Locally Stationary Processes With Applications to Testing.” Journal of the American Statistical Association.
Hegger, Kantz, Matassini, et al. 2000. “Coping with Nonstationarity by Overembedding.” Phys. Rev. Lett.
Livan, Inoue, and Scalas. 2012. “On the Non-Stationarity of Financial Time Series: Impact on Optimal Portfolio Selection.” Journal of Statistical Mechanics: Theory and Experiment.
Paparoditis. 2010. “Validating Stationarity Assumptions in Time Series Analysis by Rolling Local Periodograms.” Journal of the American Statistical Association.
Preuß, Vetter, and Dette. 2013. “A Test for Stationarity Based on Empirical Processes.” Bernoulli.
Saatçi, Turner, and Rasmussen. 2010. “Gaussian Process Change Point Models.” In Proceedings of the 27th International Conference on International Conference on Machine Learning. ICML’10.
Shalizi, Jacobs, and Clauset. n.d. “Adapting to Non-Stationarity with Growing Expert Ensembles.”
Shinohara, Manome, Suzuki, et al. 2020. “A New Method of Bayesian Causal Inference in Non-Stationary Environments.” PLOS ONE.
Thorisson. 2000. Coupling, Stationarity, and Regeneration.
van Delft, Characiejus, and Dette. 2021. “A Nonparametric Test for Stationarity in Functional Time Series.” Statistica Sinica.
van Delft, and Eichler. 2018. “Locally Stationary Functional Time Series.” Electronic Journal of Statistics.
Vogt, and Dette. 2015. “Detecting Gradual Changes in Locally Stationary Processes.” The Annals of Statistics.
Von Sachs, and Neumann. 2000. “A Wavelet-Based Test for Stationarity.” Journal of Time Series Analysis.