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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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    References listed on IDEAS

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    1. Taras Lazariv & Wolfgang Schmid, 2019. "Surveillance of non-stationary processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 305-331, September.
    2. Dette, Holger & Golosnoy, Vasyl & Kellermann, Janosch, 2022. "Correcting Intraday Periodicity Bias in Realized Volatility Measures," Econometrics and Statistics, Elsevier, vol. 23(C), pages 36-52.
    3. Golosnoy, Vasyl & Gribisch, Bastian & Seifert, Miriam Isabel, 2019. "Exponential smoothing of realized portfolio weights," Journal of Empirical Finance, Elsevier, vol. 53(C), pages 222-237.
    4. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    5. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2016. "Exploiting the errors: A simple approach for improved volatility forecasting," Journal of Econometrics, Elsevier, vol. 192(1), pages 1-18.
    6. Lazariv, Taras & Okhrin, Yarema & Schmid, Wolfgang, 2015. "Behavior of EWMA type control charts for small smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 115-125.
    7. Manuel Morais & Yarema Okhrin & Wolfgang Schmid, 2015. "Quality surveillance with EWMA control charts based on exact control limits," Statistical Papers, Springer, vol. 56(3), pages 863-885, August.
    8. Vasyl Golosnoy & Jens Hogrefe, 2013. "Signaling NBER turning points: a sequential approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 438-448, February.
    9. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    10. Olha Bodnar & Wolfgang Schmid, 2007. "Surveillance of the mean behavior of multivariate time series," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 383-406, November.
    11. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    12. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    13. Vasyl Golosnoy & Anja Rossen, 2018. "Modeling dynamics of metal price series via state space approach with two common factors," Empirical Economics, Springer, vol. 54(4), pages 1477-1501, June.
    14. Golosnoy, Vasyl & Roestel, Jan, 2019. "Real-Time Monitoring Of The Us Inflation Expectation Process," Macroeconomic Dynamics, Cambridge University Press, vol. 23(6), pages 2221-2249, September.
    15. Claudia Klüppelberg & Miriam Isabel Seifert, 2019. "Financial risk measures for a network of individual agents holding portfolios of light-tailed objects," Finance and Stochastics, Springer, vol. 23(4), pages 795-826, October.
    16. Chen, Cathy Yi-hsuan & Okhrin, Yarema & Wang, Tengyao, 2022. "Monitoring network changes in social media," LSE Research Online Documents on Economics 113742, London School of Economics and Political Science, LSE Library.
    17. Vasyl Golosnoy & Iryna Okhrin & Wolfgang Schmid, 2012. "Statistical Surveillance of Volatility Forecasting Models," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 513-543, June.
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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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