Control charts for measurement error models

Area of Science:

• Statistical Process Control
• Time Series Analysis
• Econometrics

Background:

• Linear measurement error models (MEMs) with AR(1) processes are common in applied research.
• These models can be represented as ARMA(1,1) processes, where the MA(1) parameter reflects measurement error variance.
• Monitoring changes in the MA(1) parameter is vital for the integrity of these models.

Purpose of the Study:

• To develop effective control charts for the online detection of changes in the MA(1) parameter of linear MEMs.
• To identify shifts between AR(1) and ARMA(1,1) processes in real-time.
• To assess the performance of proposed monitoring techniques.

Main Methods:

• Development of cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts.
• Utilizing Monte Carlo simulations to evaluate control chart performance.
• Application to time series data of daily realized volatilities for empirical illustration.

Main Results:

• The study successfully developed CUSUM and EWMA control charts for detecting parameter changes in MEMs.
• Simulation results indicate the effectiveness of these charts in identifying shifts between AR(1) and ARMA(1,1) processes.
• The empirical application demonstrates the practical utility of the proposed methods.

Conclusions:

• The developed control charts provide valuable tools for online monitoring of linear measurement error models.
• Timely detection of MA(1) parameter changes enhances the reliability of applied research using these models.
• The approach is robust and applicable to financial time series data like realized volatilities.