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Control charts for measurement error models.

Vasyl Golosnoy1, Benno Hildebrandt1, Steffen Köhler1

  • 1Faculty of Management and Economics, Ruhr University Bochum, Universitätsstrasse 150, 44801 Bochum, Germany.

Advances in Statistical Analysis : Asta : a Journal of the German Statistical Society
|October 10, 2022

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces control charts to monitor changes in measurement error models (MEMs). These tools detect shifts between AR(1) and ARMA(1,1) processes, crucial for accurate statistical analysis.

Keywords:
Control chartsMeasurement errorStatistical process controlVolatility modeling

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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.