Stationary process

Discussion in 'CS2' started by Kanishka, May 19, 2022.

  1. Kanishka

    Kanishka Active Member

    Is my understanding correct that any stochastic process that is iid, is a stationary process, since the variables are identically distributed?

    Please guide me if I'm wrong.
  2. CapitalActuary

    CapitalActuary Very Active Member

    A stationary process is one where the joint distribution doesn't change through time. An i.i.d. stochastic process has the same joint distribution regardless of time. So yes, it must be stationary.
  3. Kanishka

    Kanishka Active Member

    Thank you for confirming. Any series with iid variables would then be strictly stationary?
  4. CapitalActuary

    CapitalActuary Very Active Member

    The way the word 'stationary' is used usually means 'strictly stationary' in my experience.

    Do bear in mind stationary is not the same thing as i.i.d. though. Stationarity says nothing about whether the variables are independent of one another.

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