Functional estimation and change detection for nonstationary time series

TL;DR

This paper develops estimators and change detection methods for nonstationary time series, allowing for robust inference on various parameters like kurtosis and autocorrelation, with theoretical guarantees and practical validation.

Contribution

It introduces a framework for change-point detection in locally stationary time series, covering nonlinear parameters, with a bootstrap method for feasible inference and consistency proof.

Findings

The proposed estimators are consistent under mild assumptions.

The bootstrap method provides reliable inference for change detection.

Application to high-frequency asset prices demonstrates practical utility.

Abstract

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null hypothesis of no change. In this paper, estimators for integrated parameters of locally stationary time series are constructed and a corresponding functional central limit theorem is established, enabling change-point inference for a broad class of parameters under mild assumptions. The proposed framework covers all parameters which may be expressed as nonlinear functions of moments, for example kurtosis, autocorrelation, and coefficients in a linear regression model. To perform feasible inference based on the derived limit distribution, a bootstrap variant is proposed and its consistency is established. The methodology is illustrated by means of a simulation study and by an application to high-frequency asset prices.