Change-point estimation for Weibull time series with copula-based Markov models

2026-05-28

AI Summary

This study addresses the challenge of estimating structural change points in non-negative time series—such as event times or volatility—where nonlinear dynamics and asymmetric tail dependence complicate inference. The authors propose a Markov chain model based on Clayton and Joe copulas coupled with Weibull marginal distributions to jointly capture abrupt shifts in both the marginal distribution and the serial dependence structure. This work presents the first integration of a copula-based Markov model with Weibull margins for offline change-point detection. Change-point locations and model parameters are simultaneously estimated via maximum likelihood using the Newton–Raphson algorithm, and confidence intervals are constructed through parametric bootstrap. Numerical experiments demonstrate superior performance in terms of RMSE and relative error, and the method successfully identifies significant changes in both distributional and dependence structures in VIX index data during the pandemic period.

Abstract

We study offline change-point estimation for time series data exhibiting nonlinear serial dependence. To address this problem, we propose a copula-based Markov chain model with Weibull marginal distributions, which is suitable for modeling nonnegative data such as event times and volatility measures. Nonlinear dependence is incorporated through the Clayton and Joe copulas, allowing the model to capture asymmetric lower-tail and upper-tail dependence structures, respectively. We derive the corresponding likelihood function and estimate the change point and model parameters using maximum likelihood estimation implemented through the Newton--Raphson algorithm. Confidence intervals are constructed via a parametric bootstrap Monte Carlo procedure. Extensive numerical studies are conducted to evaluate the finite-sample performance and robustness of the proposed method under different dependence structures and copula misspecification scenarios. The results demonstrate that the proposed estimators perform well in terms of RMSE and relative error, particularly for the estimation of the change point. An empirical application to the VIX index during the COVID-19 pandemic further illustrates the practical usefulness of the proposed approach in detecting structural changes in both the marginal distributions and serial dependence structure.

Problem

• change-point estimation
• Weibull time series
• copula-based Markov models
• nonlinear serial dependence
• structural change

Innovation

• copula-based Markov model
• Weibull time series
• change-point estimation
• asymmetric tail dependence
• parametric bootstrap