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

Area of Science:

• Statistics
• Econometrics
• Time Series Analysis

Background:

• Structural changes in time series data can significantly impact model accuracy.
• Detecting these changes, especially in discrete-valued series with unknown distributions, presents analytical challenges.
• Existing methods may not adequately address epidemic change-point scenarios in such complex data.

Purpose of the Study:

• To develop a robust method for detecting structural changes in discrete-valued time series.
• To propose an epidemic change-point detection test based on quasi-maximum likelihood estimation.
• To establish theoretical guarantees for the proposed estimator and test statistic.

Main Methods:

• Utilizing a Poisson quasi-maximum likelihood estimator (QMLE) for models with unknown conditional distributions.
• Developing a test statistic derived from the QMLE to detect parameter changes.
• Analyzing the asymptotic properties (consistency and normality) of the QMLE.
• Investigating the behavior of the test statistic under null (no change) and alternative (epidemic change) hypotheses.

Main Results:

• Sufficient conditions for the consistency and asymptotic normality of the Poisson QMLE are established.
• A novel test statistic for epidemic change-point detection is proposed.
• Under the null hypothesis, the test statistic converges to a known distribution (Brownian bridge increments).
• The test statistic diverges under the epidemic alternative, confirming the procedure's power consistency.

Conclusions:

• The proposed Poisson QMLE provides a consistent and asymptotically normal estimator for discrete time series with changing parameters.
• The developed change-point detection test is effective and statistically sound for identifying epidemic structural breaks.
• The methodology is validated through simulations and real-world data analysis, demonstrating practical applicability.