Using local tests to estimate convergence rates for identification

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 first revisit and clarify this relationship, and propose in addition new simple proofs for stationary systems. Except for specific algorithms (e.g., regression models) estimating the convergence rate of an identification procedure is difficult. Even if there are general central limit theorems available, building the corresponding estimators in practice is not easy. We propose a practical alternative, based on the relation between identification and local testing, and we propose a bootstrap-like estimator for the convergence rate