Nonstationary ARMA models via simultaneous AR and MA estimation

A large class of nonstationary signals is efficiently modeled through time-varying autoregressive or ARMA models which are characterized by the constraint that their coefficients evolve within a subspace, a basis of functions spanning it being known prior to estimation. In this context, powerful estimators exist for AR models, and lattice filters, but for the more complex ARMA models, existing estimators are either too costly or too poor. This paper presents a new estimator which realizes a good compromise between cost and quality. The AR and MA part of the model are estimated simultaneously in order to fit the two-indices nonstationary impulse response of a long time-varying autoregressive model. In the case where the AR order is equal to the MA order plus one, the solution has a Toëplitz structure and leads to a fast algorithm.