R-estimation in semiparametric dynamic location-scale models

Abstract

We propose rank-based estimation (R-estimators) as an alternative to Gaussian quasi-likelihood and standard semiparametric estimation in time series models, where conditional location and/or scale depend on a Euclidean parameter of interest, while the unspecified innovation density is a nuisance. We show how to construct R-estimators achieving semiparametric efficiency at some predetermined reference density while preserving root-n consistency and asymptotic normality irrespective of the actual density. Contrary to the standard semiparametric estimators, our R-estimators neither require tangent space calculations nor innovation density estimation. Numerical examples illustrate their good performances on simulated and real data.