Noncausal Nonminimum Phase ARMA Modeling of Non-Gaussian Processes

A method is presented for the estimation of the parameters of a noncausal nonminimum phase ARMA model for non-Gaussian random processes. Using certain higher order cepstra slices, the Fourier phases of two intermediate sequences ( hmin(n ) and hmax(n)) can be computed, where hmin(n) is composed of the minimum phase parts of the AR and MA models, and hmax(n) of the corresponding maximum phase parts. Under the condition that there are no zero-pole cancellations in the ARMA model, these two sequences can be estimated from their phases only, and lead to the reconstruction of the AR and MA parameters, within a scalar and a time shift. The AR and MA orders do not have to be estimated separately, but they are byproduct of the parameter estimation procedure. Through simulations it is shown that, unlike existing methods, the estimation procedure is fairly robust if a small order mismatch occurs. Since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of hmin(n) and hmax(n), the phase errors due to finite length data are studied and their statistics are derived.