ADAPTATION FOR NONPARAMETRIC ESTIMATORS OF LOCALLY STATIONARY PROCESSES

Rainer Dahlhaus and Stefan Richter

Econometric Theory, 2023, vol. 39, issue 6, 1123-1153

Abstract: 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.

Date: 2023
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