On several local asymptotic properties for fractional autoregressive models with strong mixing noises

This paper is devoted to study several local asymptotic properties for fractional autoregressive models with strong mixing noises, we treat local asymptotic normality using Swensen's lemma, then we deal with local asymptotic minimaxity and local asymptotic linearity, these properties are fundamental and prepare the way for the construction of adaptive estimator. In order to measure the performance of our approach we deal with simulation study, it allows us to check the validity of the theoretical results.