Inference for Multiple Change-points in Piecewise Locally Stationary Time Series

TL;DR

This paper introduces a likelihood-based method for detecting multiple change-points in locally stationary time series, capable of identifying both abrupt and smooth changes in the data's dependence structure.

Contribution

It presents a novel approach that jointly models abrupt and smooth changes, estimating their number, locations, and types within a unified framework.

Findings

Consistent estimation of change-point number and locations.

Asymptotic distributions for jump and kink estimators.

Effective performance demonstrated through simulations and real data.

Abstract

Change-point detection and locally stationary time series modeling are two major approaches for the analysis of non-stationary data. The former aims to identify stationary phases by detecting abrupt changes in the dynamics of a time series model, while the latter employs (locally) time-varying models to describe smooth changes in dependence structure of a time series. However, in some applications, abrupt and smooth changes can co-exist, and neither of the two approaches alone can model the data adequately. In this paper, we propose a novel likelihood-based procedure for the inference of multiple change-points in locally stationary time series. In contrast to traditional change-point analysis where an abrupt change occurs in a real-valued parameter, a change in locally stationary time series occurs in a parameter curve, and can be classified as a jump or a kink depending on whether the curve is discontinuous or not. We show that the proposed method can consistently estimate the number, locations, and the types of change-points. Two different asymptotic distributions corresponding respectively to jump and kink estimators are also established. Extensive simulation studies and a real data application to financial time series are provided.