# Nonparametric Multiple Change Point Detection for Non-Stationary Times Series

## TL;DR

This paper introduces a nonparametric method for detecting multiple change points in non-stationary time series by comparing spectral density functions, applicable to various linear processes, with proven consistency and empirical validation.

## Contribution

It proposes a novel nonparametric approach for change point detection that works for a wide class of linear processes, including non-invertible models, with consistent estimation and model selection.

## Key findings

- Method accurately detects change points in simulations.
- Approach is effective for both invertible and non-invertible processes.
- Consistent estimation of number and locations of change points.

## Abstract

This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral density functions are different. The theory is based on the assumption that within each segment, time series is a linear process, which means that our method works not only for classic time series models, e.g., causal and invertible ARMA process, but also preserves good performance for non-invertible moving average process. We show that our estimations for change points are consistent. Also, a Bayesian information criterion is applied to estimate the member of change points consistently. Simulation results as well as empirical results will be presented.