CONSISTENT ESTIMATION OF SYSTEM ORDER

We consider a parameterized family [formula omitted], of systems or sources having stochastic outputs {χ} that are partially described by a statistic (e.g., correlation function) Σ(τ). If we represent [formula omitted], then by the system order Ma we mean the index n of the last nonzero term in die expansion of a. Our objective is to generate a sequence [formula omitted] of estimates of the true Mao that converge to it at least in probability. We provide conditions ensuring the existence of such a statistically consistent sequence of estimators, as well as improved conditions yielding convergence in mean-square and with probability one. We establish existence by providing a method for constructing a family of consistent estimators of system order. We then apply our method to estimate the order of a scalar moving averages process and the order of a scalar autoregressive process. Our present results are primarly of a theoretical nature, as we lack the efficiency and simulation studies desirable in support of a practical estimator of system order. Copyright © 1979 by The Institute of Electrical and Electronics Engineers, Inc.