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- Strongly stationary
- If the joint distribution of is the same as the joint distribution of
- Weakly stationary
- Also called second-order stationary.
If the conditions below are satisfied:
No assumptions need to be made for higher moments.
Your data sample is , a realization of the joint distribution .
This stationary condition is necessary for applying the methods
described in this section, since it is required by most of the
detailed derivations, especially the Wiener-Khintchine theorem (see 2.4).
Is your time series (weakly) stationary?
- Detrend the data first.
- Think about if the conditions are unchanged for the entire interval when the signals were recorded.
- The change of perturbation amplitude with time does not necessarily mean that your time series is not (weakly) stationary.