Hidden Markov models (HMM's) are successfully applied in various fields of
time series analysis. Colored noise, e.g,, due to filtering, violates basic
assumptions of the model. Although it is well known how to consider autore
gressive (AR) filtering, there is no algorithm to take into account moving-
average (MA) filtering in parameter estimation exactly. We present an appro
ximate likelihood estimator for MA-filtered HMM that is generalized to deal
with an autoregressive moving-average (ARMA) filtered HMM. The approximati
on order of the likelihood calculation can be chosen. Therefore, we obtain
a sequence of estimators for the HMM parameters as well as for the filter c
oefficients. The recursion equations for an efficient algorithm are derived
from exact expressions for the forward iterations. By simulations, we show
that the derived estimators are unbiased in filter situations where standa
rd HMM's are not able to recover the true dynamics, Special inplementation
strategics together with small approximations yield further acceleration of
the algorithm.