On the relationship between identification and local tests

Convergence rates and related central limit theorems have been the subject of numerous papers. In Benveniste et al. (1987) a systematic link was first established between system identification, and model validation or testing for small changes. Similarities and relations are discussed in Benveniste et al. (1990), and this so-called local approach has proved very successful in practical applications. In this paper, we revisit and clarify this relationship, and propose in addition new simple proofs for stationary systems.