Testing for change points in time series models and limiting theorems for NED sequences

TL;DR

This paper develops theoretical tools for detecting change points in time series, establishing strong laws and invariance principles for NED sequences, and applies these to fractional ARIMA models.

Contribution

It introduces new limiting theorems for NED sequences and applies them to change point testing in complex time series models.

Findings

Established strong law of large numbers for NED sequences

Developed a strong invariance principle for forward and backward sums

Verified assumptions for fractional ARIMA models

Abstract

This paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near-epoch dependent sequences. Using these limiting theorems, we develop a general asymptotic theory on the Wald test for change points in a general class of time series models under the no change-point hypothesis. As an application, we verify our assumptions for the long-memory fractional ARIMA model.