On the consistency and asymptotic normality of discrete-time LTI models identified from concatenated data sets

Even-though data concatenation is a well-known technique for identifying Linear Time-Invariant models from multiple records, the study of the asymptotic properties of the estimator continues to be limited. Therefore, we investigated consistency and asymptotic normality as the number or records tend to infinity, with focus on the identification of discrete-time parametric models for single-input single-output systems operating in open loop. This paper presents the results of a consistency and asymptotic normality study based on the analysis of the prediction error cost function and Monte Carlo simulations. We show that for persistently exciting input signals (filtered white noise), model structures such as Output-Error, AR and ARX are consistently estimated, and the estimated parameters are asymptotically normally distributed. On the other hand, ARMA, ARMAX and Box-Jenkins present a bias on the estimated parameters. However, this bias asymptotically disappears for longer records (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the consistency and asymptotic normality of data concatenation for identifying Linear Time-Invariant models. The results show that certain model structures are consistently estimated and the estimated parameters are asymptotically normally distributed when input signals are persistently exciting. However, some model structures exhibit a bias in the estimated parameters, which asymptotically disappears for longer records.