A Robust ARX and ARMA Model order Estimation via Pivot-Neighbors Comparisons

Model order selection of an Autoregressive Moving Average (ARMA) process is an important problem. This paper presents a new algorithm for the estimation of an ARMA and autoregressive with exogenous input (ARX) model orders based on a rounding approach which uses the floor and the ceiling functions. The rounding approach is implemented to deal with the precision of binary words. The proposed algorithm is based on selecting a sequence of pivot cells from an MEV matrix which is based on the minimum eigenvalue of a covariance matrix computed from the observed data. It searches for the corner that contains the estimates of the true orders using the floor and the ceiling functions of the pivot cell values and the values of its neighbors. The proposed algorithm is an expansion of the algorithm proposed by Liang et al. (IEEE Transaction on Signal Processing, 1993; 41(10): 3003-3009). Recent patents and research advances aim to apply eigenvalue decomposition in estimation and prediction. Among the patents discussed is a method that describes estimation of uncertainty of a measuring machine where covariance matrix is subjected to eigenvalue decomposition.