ADAPTATION FOR NONPARAMETRIC ESTIMATORS OF LOCALLY STATIONARY PROCESSES

Two adaptive bandwidth selection methods for minimizing the mean squared error of nonparametric estimators in locally stationary processes are proposed. We investigate a cross-validation approach and a method based on contrast minimization and derive asymptotic properties of both methods. The results are applicable for different statistics under a general setting of local stationarity including nonlinear processes. At the same time, we deepen the general framework for local stationarity based on stationary approximations. For example, a general Bernstein inequality is derived for such processes. The properties of the bandwidth selection methods are also investigated in several simulation studies.