Adaptation for nonparametric estimators of locally stationary processes

TL;DR

This paper introduces two adaptive bandwidth selection methods for nonparametric estimators in locally stationary processes, providing theoretical analysis and simulation validation for broad classes of processes.

Contribution

It develops and analyzes two novel adaptive bandwidth selection techniques for nonparametric estimation in locally stationary processes, including nonlinear cases.

Findings

Both methods perform well in simulations.

Asymptotic properties are rigorously derived.

Framework extends to nonlinear and broad locally stationary processes.

Abstract

Two adaptive bandwidth selection methods for 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 broad setting of locally 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. A simulation study performed on the covariance function and more complicated functionals shows that both adaptation methods work well.