ARMA models realization and impulse responses

A parallel is made between the role played by covariances in the determination of auto-regressive models and the role played by impulse responses in the determination of ARMA models. Auto-regressive models are known to maximize the Burg-entropy under covariance constraints. Auto-regressive-moving-average models give the maximum of the Burg-entropy among processes sharing the same covariances and impulse responses up to a certain lag. Such models are constructed by iterative or algebraic methods under the different constraints. A new recursive method of identification of the order of an ARMA model is also developed, based on the generalized Reflection coefficients.