Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2022 Oct 5:1-20.
doi: 10.1007/s10182-022-00462-8. Online ahead of print.

Control charts for measurement error models

Vasyl Golosnoy  1 , Benno Hildebrandt  1 , Steffen Köhler  1 , Wolfgang Schmid  2 , Miriam Isabel Seifert  1
Affiliations

Control charts for measurement error models

Vasyl Golosnoy et al. Adv Stat Anal. .

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.

Keywords: Control charts; Measurement error; Statistical process control; Volatility modeling.

PubMed Disclaimer

Figures

Fig. 1
Fig. 1
Signals for S&P500: EWMA (red), CUSUM (blue) with charts based on in sample (left) and full sample (right) parameter estimates (colour figure online)
Fig. 2
Fig. 2
Signals for DAX 30: EWMA (red), CUSUM (blue) with charts based on in sample (left) and full sample (right) parameter estimates (colour figure online)
Fig. 3
Fig. 3
Signals for Nikkei 225: EWMA (red), CUSUM (blue) with charts based on in sample (left) and full sample (right) parameter estimates (colour figure online)
See this image and copyright information in PMC

References

    1. Andersen TG, Bollerslev T, Diebold FX, Ebens H. The distribution of realized stock return volatility. J. Financ. Econ. 2001;61(1):43–76. doi: 10.1016/S0304-405X(01)00055-1. - DOI
    1. Barndorff-Nielsen O, Shephard N. Econometric analysis of realized volatility and its use in estimating stochastic volatility models. J. Roy. Stat. Soc. B. 2002;64:253–280. doi: 10.1111/1467-9868.00336. - DOI
    1. Bodnar O, Schmid W. Surveillance of the mean behaviour of multivariate time series. Stat. Neerl. 2007;61:383–406. doi: 10.1111/j.1467-9574.2007.00365.x. - DOI
    1. Bollerslev T, Patton AJ, Quaedvlieg R. Exploiting the errors: a simple approach for improved volatility forecasting. J. Econ. 2016;192:1–18. doi: 10.1016/j.jeconom.2015.10.007. - DOI
    1. Brockwell PJ, Davis RA. Time Series: Theory and Methods. Berlin: Springer; 2009.

LinkOut - more resources