A number of approaches are available to estimate ARMA parameters from the data .
The approach we prefer operates using a recursion.
We first assume the process is AR only and estimate
We then estimate
from the sequence
Next, is re-estimated from
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 frequency-domain PDF
is possible using the approach in (section 16.5).
For this we need the CR bound analysis.