Control charts for measurement error models

Vasyl Golosnoy (), Benno Hildebrandt (), Steffen Köhler (), Wolfgang Schmid () and Miriam Isabel Seifert ()
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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

AStA Advances in Statistical Analysis, 2023, vol. 107, issue 4, No 4, 693-712

Abstract: 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: Statistical process control; Measurement error; Control charts; Volatility modeling (search for similar items in EconPapers)
JEL-codes: C22 C44 C58 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10182-022-00462-8

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