Monitoring parameter change for bivariate time series models of counts.

Area of Science:

• Statistics
• Time Series Analysis
• Econometrics

Background:

• Detecting parameter changes in time series is crucial for accurate modeling.
• Bivariate count time series models, such as BIGARCH and BINAR, are widely used but require robust monitoring procedures.
• Existing methods may not adequately address parameter instability in these specific models.

Purpose of the Study:

• To develop an effective online monitoring procedure for detecting parameter changes in bivariate count time series.
• To apply cumulative sum (CUSUM) processes to residuals from BIGARCH and BINAR models for change detection.
• To establish theoretical control limits for the proposed monitoring technique.

Main Methods:

• Utilizing standardized residuals derived from bivariate integer-valued generalized autoregressive heteroscedastic (BIGARCH) and autoregressive (BINAR) models.
• Constructing a cumulative sum (CUSUM) process based on these residuals for online monitoring.
• Developing limit theorems to derive appropriate control limits for the CUSUM process.

Main Results:

• The proposed CUSUM-based monitoring procedure effectively detects parameter changes in bivariate count time series.
• Limit theorems provide a theoretical foundation for setting control limits, ensuring reliable detection.
• Simulation studies and real data analysis demonstrate the practical validity and performance of the method.

Conclusions:

• The developed online monitoring procedure offers a statistically sound approach for detecting parameter shifts in BIGARCH and BINAR models.
• The method is validated through empirical studies, showing its utility in real-world applications.
• This work contributes to the field of statistical process control for complex count data time series.