CONTRAST ESTIMATION OF GENERAL LOCALLY STATIONARY PROCESSES USING COUPLING

This paper aims at providing statistical guarantees for a kernel based estimation of time varying parameters driving the dynamic of local stationary processes. We extend the results of Dahlhaus et al. [13] considering the local stationary version of the infinite memory processes of Doukhan and Wintenberger [22]. The estimators are computed as localized M-estimators of any contrast satisfying appropriate contraction conditions.We prove the uniform consistency and pointwise asymptotic normality of such kernel based estimators. We apply our result to usual contrasts such as least-square, least absolute value, or quasi-maximum likelihood contrasts.