Robust Change Point Test for General Integer-Valued Time Series Models Based on Density Power Divergence.

Area of Science:

• Time Series Analysis
• Statistical Inference
• Robust Statistics

Background:

• Parameter change detection is crucial in time series analysis.
• Traditional methods are sensitive to outliers in data.
• Integer-valued time series models are common in various fields.

Purpose of the Study:

• To develop a robust test for parameter change detection in integer-valued time series.
• To address the challenge of data contamination by outliers.
• To utilize density power divergence for robust estimation and testing.

Main Methods:

• Employing a robust change point test based on density power divergence (DPD).
• Utilizing the minimum density power divergence estimator (MDPDE) as the objective function.
• Deriving the limiting null distribution of the DPD-based test.

Main Results:

• The DPD-based test exhibits robustness against outliers.
• The limiting null distribution of the test is a function of a Brownian bridge.
• Monte Carlo simulations confirm the test's reliable performance.

Conclusions:

• The proposed DPD-based test is effective for detecting parameter changes in contaminated integer-valued time series.
• The test demonstrates robust properties inherited from MDPDE and DPD.
• The methodology is validated through a real-world financial time series analysis.