Inference for Multiple Change-points in Linear and Non-linear Time Series Models

TL;DR

This paper introduces a computationally efficient generalized likelihood ratio scan method for detecting multiple change-points in both linear and nonlinear time series, providing estimates and confidence intervals with proven consistency.

Contribution

The paper presents a novel GLRSM approach for multiple change-point detection that is computationally efficient and theoretically consistent, applicable to complex time series models.

Findings

Method effectively detects multiple change-points in simulations.

Computational complexity is as low as O(n(log n)^3).

Estimates of change-points are consistent.

Abstract

In this paper we develop a generalized likelihood ratio scan method (GLRSM) for multiple change-points inference in piecewise stationary time series, which estimates the number and positions of change-points and provides a confidence interval for each change-point. The computational complexity of using GLRSM for multiple change-points detection is as low as $O(n(\log n)^3)$ for a series of length $n$. Consistency of the estimated numbers and positions of the change-points is established. Extensive simulation studies are provided to demonstrate the effectiveness of the proposed methodology under different scenarios.