Adaptiveness in Time Series Models

Résumé du livre

Abstract: "Many time series are modelled by stationary processes via innovations that are independent of the past. Suppose the parameter of interest is unrelated to the distribution of the innovations. We compare the estimation problem of this parameter of interest within a purely parametric framework to estimation within a semiparametric model where the shape of the distribution of the innovations appears as a non-Euclidean nuisance parameter. Typically the asymptotic estimation problem is equally hard in both models, mainly due to the independence of innovations and past. We illustrate this phenomenon in several well-known time series models."