ARMA parameter estimation

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 $ {\bf a}= [a_1, \ldots a_P]$ and $ \sigma^2$. We then estimate $ {\bf b}= [b_1, \ldots b_P]$ from the sequence

$\displaystyle u_n = \sum_{i=0}^P \; a_i \; x_{n-i}.$ (9.20)

Next, $ {\bf a}$ is re-estimated from

$\displaystyle v_n = -\sum_{i=1}^P \; b_i \;v_{n-i} + x_n.$ (9.21)

The algorithm works by alternately estimating $ {\bf b}$ from the sequence that has the AR component removed, then $ {\bf a}$ 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 (9.18) is possible using the approach in (section 16.5). For this we need the CR bound analysis.

Baggenstoss 2017-05-19