Detecting multiple change-points in general causal time series using penalized quasi-likelihood

TL;DR

This paper introduces a penalized quasi-likelihood method for off-line detection of multiple change-points in complex causal time series models, demonstrating consistency and improved convergence rates.

Contribution

It develops a new penalized contrast approach for detecting multiple change-points in a broad class of semiparametric causal time series models, with proven consistency and enhanced convergence properties.

Findings

Method achieves consistency under Lipshitzian conditions.

Convergence rates match those of independent data when r≥4.

Improves upon existing results for AR(∞), ARCH(∞), TARCH(∞) models.

Abstract

This paper is devoted to the off-line multiple change-point detection in a semiparametric framework. The time series is supposed to belong to a large class of models including AR($\infty$), ARCH($\infty$), TARCH($\infty$),... models where the coefficients change at each instant of breaks. The different unknown parameters (number of changes, change dates and parameters of successive models) are estimated using a penalized contrast built on conditional quasi-likelihood. Under Lipshitzian conditions on the model, the consistency of the estimator is proved when the moment order $r$ of the process satisfies $r\geq 2$. If $r\geq 4$, the same convergence rates for the estimators than in the case of independent random variables are obtained. The particular cases of AR($\infty$), ARCH($\infty$) and TARCH($\infty$) show that our method notably improves the existing results.