Actually I am asking this question especially for subsurface pressure data of an oil well (pressure will vary according to the flow rate). Nonetheless, any kind of method that works for non-stationary time series data will be sufficient. For the sake of the question, we can assume the data is noiseless.
Fehmi Özbayrak Nonstationarity also depends on the kernel density estimates, and may not reject stationarity when m is small. Log-spline bivariate density estimation and LLDM by Loader may also be considered to improve tail estimation, in the presence of moderate to low values of m.
https://www.researchgate.net/publication/323694683_Anomaly_Detection_in_Streaming_Nonstationary_Temporal_Data
This is a paper in this area.
Fehmi Özbayrak Nonstationarity also depends on the kernel density estimates, and may not reject stationarity when m is small. Log-spline bivariate density estimation and LLDM by Loader may also be considered to improve tail estimation, in the presence of moderate to low values of m.
See the link: Robust statistics: theory and methods with R | Maronna, Ricardo A, Martin R.D., Yohai V.J. | download (b-ok.cc) R D Martin was one of the major developers in this subject. Best, D. Booth
The previous answers are related to either extreme value theory and robustness. Another approach is based on outlier detection. Several statistical packages have outlier detection capabilities like SAS, SPSS TSMODEL, Tramo-Seats and R (the tsoutlier package).
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