Solved – Why is ARMA used to model a stationary process

stochastic-processestime series

Under certain condition, an ARMA model is stationary.

  1. But I was wondering why an ARMA model can (always?) be used to model
    a stationary process in time series?

    • Is any stationary process an ARMA process? Or, for any stationary
      process, is there an ARMA process s.t. they are identical a.s., or
      have the same law, or they are the same in some other sense?
    • Or for any stationary process, is there a sequence of ARMA processes
      which converges to the stationary process in some sense?
  2. Or is there a stationary process which is not a ARMA process, or
    cannot be modelled as ARMA?

Best Answer

It's mainly by definition. You use ARMA if the series is stationary. If it is not stationary, you can convert the series into a stationary process by taking the nth difference, in this case the ARMA model becomes an ARIMA.

Hope this helps.

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