Epidemic change-point detection in general causal time series

TL;DR

This paper introduces a new statistical test for detecting epidemic change-points in a wide range of causal time series models, including AR, ARCH, and GARCH processes, using Gaussian quasi-maximum likelihood estimation.

Contribution

It proposes a novel test statistic based on Gaussian QMLE that effectively detects epidemic changes in complex causal time series models.

Findings

Test statistic converges to a Brownian bridge distribution under null hypothesis.

Test statistic diverges under epidemic change, enabling detection.

Numerical simulations and real data examples validate the method.

Abstract

We consider an epidemic change-point detection in a large class of causal time series models, including among other processes, AR($\infty$), ARCH($\infty$), TARCH($\infty$), ARMA-GARCH. A test statistic based on the Gaussian quasi-maximum likelihood estimator of the parameter is proposed. It is shown that, under the null hypothesis of no change, the test statistic converges to a distribution obtained from a difference of two Brownian bridge and diverges to infinity under the epidemic alternative. Numerical results for simulation and real data example are provided.