I understand that a (weakly) stationary time series is one where

  1. $E[X_t]$ = constant

  2. $Var(x_t)$ = constant

  3. $cov(x_t,x_{t-h})$ = constant, at any h (regardless of t)

and that ARMA models can only be applied on data that is stationary. Then, I learnt that for a AR(1) model to be stationary, the coefficient $|\phi_1|$ has to be less than 1.

What does it mean for a "model" to be stationary? Does it just mean that the data we have applied the model to is stationary? Or is it something else?

  • 4
    $\begingroup$ It's just loose wording, not really important most of the time. An AR(1) process is stationary if and only if $|\phi_1| < 1$. If we model actual data, we have an AR(1) model of the underlying data generating process, so some people (apparently) refer to the model as if it were the process itself, which it isn't, but after a while you get used to such sloppiness and you know what they mean. $\endgroup$
    – jbowman
    Jan 18, 2018 at 4:18


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