# Cross validation for locally stationary processes

## TL;DR

This paper introduces an adaptive cross-validation method for selecting bandwidths in local M-estimators applied to locally stationary processes, demonstrating asymptotic optimality and practical effectiveness through simulations.

## Contribution

It presents a novel cross-validation approach for bandwidth selection in locally stationary processes, with proven asymptotic optimality and broad applicability.

## Key findings

- Method achieves asymptotic optimality under mild conditions
- Works well even in misspecified models
- Applicable to both linear and nonlinear processes

## Abstract

We propose an adaptive bandwidth selector via cross validation for local M-estimators in locally stationary processes. We prove asymptotic optimality of the procedure under mild conditions on the underlying parameter curves. The results are applicable to a wide range of locally stationary processes such linear and nonlinear processes. A simulation study shows that the method works fairly well also in misspecified situations.