Change point detection in heteroscedastic time series

TL;DR

This paper introduces a robust framework for detecting change points in the mean of heteroscedastic time series, accommodating changing variability and serial dependence, with theoretical foundations and practical applications.

Contribution

It develops a new functional central limit theorem for dependent variables with changing variance and applies it to create change point tests that are robust to heteroskedasticity and dependence.

Findings

Tests are robust to heteroskedasticity and serial dependence.

Simulation studies demonstrate good finite sample performance.

Application to US treasury yields illustrates practical utility.

Abstract

Many time series exhibit changes both in level and in variability. Generally, it is more important to detect a change in the level, and changing or smoothly evolving variability can confound existing tests. This paper develops a framework for testing for shifts in the level of a series which accommodates the possibility of changing variability. The resulting tests are robust both to heteroskedasticity and serial dependence. They rely on a new functional central limit theorem for dependent random variables whose variance can change or trend in a substantial way. This new result is of independent interest as it can be applied in many inferential contexts applicable to time series. Its application to change point tests relies on a new approach which utilizes Karhunen--Lo{\'e}ve expansions of the limit Gaussian processes. After presenting the theory in the most commonly encountered setting of the detection of a change point in the mean, we show how it can be extended to linear and nonlinear regression. Finite sample performance is examined by means of a simulation study and an application to yields on US treasury bonds.