  Discrete-time input/output models, also called infinite impulse response
(IIR) models or autoregressive moving average (ARMA) models, are useful for
online identification as they can be efficiently updated using recursive least
squares (RLS) as new data is collected. Several works have studied the
convergence of the input/output model coefficients identified using RLS under
the assumption that the order of the identified model is the same as that of
the true system. However, the case of model order mismatch is not as well
addressed. This work begins by introducing the notion of \textit{equivalence}
of input/output models of different orders. Next, this work analyzes online
identification of input/output models in the case where the order of the
identified model is higher than that of the true system. It is shown that,
given persistently exciting data, the higher-order identified model converges
to the model equivalent to the true system that minimizes the regularization
term of RLS.
