Detecting stationarity in stochastic processes

Change-points, trends and transients

November 29, 2021 — April 1, 2022

Hilbert space
kernel tricks
metrics
signal processing
statistics
stochastic processes
Figure 1

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

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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.
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Hegger, Kantz, Matassini, et al. 2000. “Coping with Nonstationarity by Overembedding.” Phys. Rev. Lett.
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van Delft, Characiejus, and Dette. 2021. “A Nonparametric Test for Stationarity in Functional Time Series.” Statistica Sinica.
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