Prony estimation of AR parameters of an ARMA time series

Abstract

The auto-covariance function of a white noise excited time series can be decomposed into the contributions of different modes, therefore having the same structure as that of the impulse response of a deterministic system. By matching the auto-covariance of the data with that of the ARMA model, the estimation of the characteristic roots of the system and the dispersion coefficients can be implemented using the Prony method, therefore the estimation of the AR parameters becomes a linear least squares problem. It is found that this estimate for the AR parameters of an ARMA model is identical to the asymptotically unbiased estimate using modified Yule-Walker equation for ARMA (n, n-1).