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Control charts for measurement error models

Author

Listed:
  • Vasyl Golosnoy

    (Ruhr University Bochum)

  • Benno Hildebrandt

    (Ruhr University Bochum)

  • Steffen Köhler

    (Ruhr University Bochum)

  • Wolfgang Schmid

    (European University Viadrina)

  • Miriam Isabel Seifert

    (Ruhr University Bochum)

Abstract

We consider a linear measurement error model (MEM) with AR(1) process in the state equation which is widely used in applied research. This MEM could be equivalently re-written as ARMA(1,1) process, where the MA(1) parameter is related to the variance of measurement errors. As the MA(1) parameter is of essential importance for these linear MEMs, it is of much relevance to provide instruments for online monitoring in order to detect its possible changes. In this paper we develop control charts for online detection of such changes, i.e., from AR(1) to ARMA(1,1) and vice versa, as soon as they occur. For this purpose, we elaborate on both cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts and investigate their performance in a Monte Carlo simulation study. The empirical illustration of our approach is conducted based on time series of daily realized volatilities.

Suggested Citation

  • Vasyl Golosnoy & Benno Hildebrandt & Steffen Köhler & Wolfgang Schmid & Miriam Isabel Seifert, 2023. "Control charts for measurement error models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(4), pages 693-712, December.
    • Handle: RePEc:spr:alstar:v:107:y:2023:i:4:d:10.1007_s10182-022-00462-8
    DOI: 10.1007/s10182-022-00462-8
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    More about this item

    Keywords

    Statistical process control; Measurement error; Control charts; Volatility modeling;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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