The most common cause of violation of stationarity are trends in mean, which can be due either to the presence of a unit root or of a deterministic trend.
32.
The authors further argue that rather than using Box Jenkins, it is better to use state space methods, as stationarity of the time series is then not required.
33.
:The proposed solution in the geostatistical formalism consists in assuming various degrees of stationarity in the random function, in order to make possible the inference of some statistic values.
34.
Stationarity is the property of a random process which guarantees that its statistical properties, such as the mean value, its moments and variance, will not change over time.
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:* Caers also use the assumption of stationarity in the context of multiple-point geostatistics, where higher n-point statistics are assumed to be stationary in the spatial domain.
36.
This focus on the vis viva by the continental physicists eventually led to the discovery of stationarity principles governing mechanics, such as the D'Alembert's principle and Hamiltonian formulations of mechanics.
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These two models can be combined into an autoregressive-moving average ( ARMA ) model, or an autoregressive-integrated-moving average ( ARIMA ) model if non-stationarity is involved.
38.
The hypothesis of stationarity related to the second moment is defined in the following way : the correlation between two random variables solely depends on the spatial distance between them, and is independent of their location:
39.
The final assumption about stationarity is difficult to test from data for a single site because of the large uncertainties in even the longest flood records and that managing flood risks in the future will become even more difficult.
40.
Any time-invariant operations also preserves AEP, stationarity and ergodicity and we may easily turn a stationary process to non-stationary without losing AEP by nulling out a finite number of time samples in the process.
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