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is not necessarily strictly stationary. Let be a random variable uniformly distributed in the interval and define the time series by
:

Then
: So is a white noise in the weak sense (the mean and cross-covariances are zero, and the variances are all the same), however it is not strictly stationary.

Nth-order stationarity

In , the distribution of samples of the stochastic process must be equal to the distribution of the samples shifted in time for all . th-order stationarity is a weaker form of stationarity

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