A Sharp Signal-to-Noise Threshold for Quasi-Maximum Likelihood Breakpoint Estimation

2026-09-10

AI Summary

本文针对多变量时间序列中的主要断点估计问题，提出了一个准最大似然估计的信号噪声比阈值准则，并通过路径框架和对数行列式目标函数的岭正则化方法来实现。

Abstract

We establish a sharp pathwise signal-to-noise criterion for quasi-maximum-likelihood (QML) estimation of a dominant breakpoint in the second-moment structure of a multivariate time series: the QML estimator is consistent whenever the between-regime contrast exceeds the within-regime fluctuation by an explicit factor, and below this threshold global recovery can fail. Two innovations drive the result. First, the framework is pathwise: no stochastic model is imposed on the data. Second, the log-determinant objective carries an additive ridge regularization: it removes the endpoint boundary layers, so no trimming of the candidate set is required, and tuning the ridge weakens the consistency condition. As an application of the main theorem, we establish consistency of QML breakpoint estimation in pervasive factor models whose dimension diverges with the sample size, for completely general error terms -- not necessarily independent, idiosyncratic, or even random.

Problem

• Quasi-Maximum Likelihood
• Breakpoint Estimation
• Signal-to-Noise Threshold
• Multivariate Time Series

Innovation

• pathwise signal-to-noise criterion
• ridge regularization
• quasi-maximum-likelihood (QML) estimation