Data-adaptive higher order ARMA model order estimation

A new method for estimating the order of a non-Gaussian autoregressive moving average (ARMA) process using higher order statistics is presented. The observed signal may be contaminated by additive, zero mean, Gaussian noise. The proposed algorithm uses third-order computations, and is based on the minimum eigenvalue of a family of covariance matrices derived from the observed data. One of the novel features of this approach is that the authors avoid nonstationary effects due to finite-length observations, thus they work with data matrices rather than calculated cumulants. This is a generalization of the approach of Liang et al. [1993] and Liang [1992], which eliminates the estimation of the a_i and b_i coefficients. Only the model orders are estimated. In theory, this approach should outperform the original work of Liang at low SNRs, since cumulants are blind to Gaussian noise. The new algorithm is applied to both ARMA and autoregressive with exogenous input (ARX) models. Examples are presented to illustrate the effectiveness of the technique