Asymptotic properties of least-squares estimates of Hammerstein-Wiener models

Abstract

This paper investigates the asymptotic properties of least squares estimates of Hammerstein-Wiener model structures, and in doing so establishes consistency and asymptotic normality under fairly mild conditions on the additive noise process, the inputs and the static non-linearities. In relation to the asymptotic distributional results, a consistent procedure for the estimation of the asymptotic variance of the parameter estimates is provided. A key theme of this paper is to demonstrate how recent results from the econometrics literature may be employed in an engineering setting. In this respect the Hammerstein-Wiener model structure serves as a demonstration example. A simulation study complements the theoretical findings.