Identification of parameter bounds for ARMAX models from records with bounded noise

Abstract

The computation of bounds on the parameters, rather than point estimates and covarianccs, is considered for autoregressive-moving-average-exogenous (ARMAX) models. The bounds derive from observations affected by bounded noise. The influence of noise structure on the performance of the best-known parameter-bounding algorithm is examined. A problem analogous to the bias in least-squares estimates when regressors and noise are mutually correlated is also found to arise in parameter-bounding. An explanation is offered, and the possibility of ARMAX parameter bounds being non-convex is pointed out.