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

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.