A number of approaches are available to estimate ARMA parameters from the data [25].
The approach we prefer operates using a recursion.
We first assume the process is AR only and estimate
and .
We then estimate
from the sequence

(9.20) 
Next, is reestimated from

(9.21) 
The algorithm works by alternately estimating from the sequence that has the
AR component removed, then from the sequence that has the
MA component removed. See software/get_arma.m. As a last step, refinement of the estimate by maximizing
the exact PDF (9.6) or the approximate frequencydomain PDF
(9.18)
is possible using the approach in (section 16.5).
For this we need the CR bound analysis.
Baggenstoss
20170519