On the Relationship between Identification and Local Tests

Convergence rates and related Central Limit theorems have been the subject of numerous papers. In 1] a systematic link was rst established between 1/ system identiication, and 2/ model validation or testing for small changes. Similarities and relations are discussed in 2], part I, chap 5, 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. Identiication et tests locaux R esum e : On r eexamine les liens entre l'identiication et les tests par le biais des m ethodes locales. Une approche originale est propos ee.