Monitoring Parameter Change for Time Series Models of Counts Based on Minimum Density Power Divergence Estimator

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Integer-valued generalized autoregressive heteroscedastic (INGARCH) models are crucial for analyzing count time series data.
• Detecting parameter changes in these models is essential for maintaining model accuracy and reliability.
• Traditional methods can be sensitive to outliers, potentially compromising monitoring performance.

Purpose of the Study:

• To develop and validate a novel online monitoring procedure for INGARCH models.
• To enhance robustness against outliers in parameter change detection.
• To utilize the strengths of minimum power divergence estimators (MDPDE) for improved statistical monitoring.

Main Methods:

• The study employs a cumulative sum (CUSUM) of score functions derived from objective functions.
• The minimum power divergence estimator (MDPDE), which includes the maximum likelihood estimator (MLE), is used for robustness.
• The proposed CUSUM procedure is designed to inherit the outlier robustness of the MDPDE.

Main Results:

• The proposed online monitoring procedure demonstrates effective detection of parameter changes in INGARCH models.
• The method exhibits robustness against outliers, a key advantage over standard techniques.
• Simulation studies and real data analysis confirm the practical validity and performance of the procedure.

Conclusions:

• The developed online monitoring procedure offers a robust and reliable approach for detecting parameter changes in INGARCH models.
• The use of MDPDE significantly enhances the procedure's resilience to outliers.
• This method provides a valuable tool for time series analysis and statistical process control.