Epidemic change-point detection in general integer-valued time series

ABSTRACT

In this paper, we consider the structural change in a class of discrete valued time series, where the true conditional distribution of the observations is assumed to be unknown. The conditional mean of the process depends on a parameter ${\theta }^{\ast }$ which may change over time. We provide sufficient conditions for the consistency and the asymptotic normality of the Poisson quasi-maximum likelihood estimator (QMLE) of the model. We consider an epidemic change-point detection and propose a test statistic based on the QMLE of the parameter. Under the null hypothesis of a constant parameter (no change), the test statistic converges to a distribution obtained from increments of a Browninan bridge. The test statistic diverges to infinity under the epidemic alternative, which establishes that the proposed procedure is consistent in power. The effectiveness of the proposed procedure is illustrated by simulated and real data examples.

KEYWORDS:

• Discrete valued time series
• change-point detection
• epidemic alternative
• semi-parametric statistic
• Poisson QMLE

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62M10
• 62F03
• 62F12

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author was supported by the CY Advanced Studies (CY Cergy Paris Université, France), and the MME-DII Center of Excellence [grant number ANR-11-LABEX-0023-01]. The second author developed within [grant number ANR BREAKRISK: ANR-17-CE26-0001-01] and the CY Initiative of Excellence [grant 'Investissements d'Avenir' ANR-16-IDEX-0008, Project 'EcoDep' PSI-AAP2020-0000000013].