I have read that an AR(p) process is stationary if all of the roots of it's characteristic equation are greater than one in absolute value.

Does this mean that I can find out if my data set is stationary by the following two methods:

A) Fit the data to AR(1), AR(2), ... , AR(n) processes with regression, approximate the roots of the characteristic equations of these processes, and check if the absolute value of roots are greater than one.

B) Fit the data to AR(1), AR(2), ... , AR(n) processes, and check if the error terms are white noise.

This is assuming the data is fit well by an AR process, but that I do not know the correct value of p.

I could also difference the data and repeat the process if the above fails.

Also, would it make any sense to fit the partial correlations to a sine wave or exponential to help determine if the data is an AR(p) process?

  • 1
    $\begingroup$ Fit model (flexible) to data (fixed), not data to a model. $\endgroup$ Jun 13, 2019 at 17:25
  • 1
    $\begingroup$ This question can be useful. $\endgroup$
    – Yves
    Jun 13, 2019 at 18:51
  • $\begingroup$ Thanks for the correction @RichardHardy $\endgroup$
    – Frank
    Jun 13, 2019 at 19:54


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