Optimal Multivariate EWMA Chart for Detecting Common Change in Mean

Yanhong Wu () and Wei Biao Wu
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Yanhong Wu: California State University Stanislaus
Wei Biao Wu: University of Chicago

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 2, 1-22

Abstract: Abstract After accurately approximating the average in-control run length ( $$ARL_0$$ A R L 0 ) for a multivariate Exponential Weighted Moving Average (EWMA) chart, we explore the optimal design of the weight parameter to minimize the stationary average delay detection time (SADDT). We conduct numerical comparisons of SADDT between Moving Average (MA), Cumulative Sum (CUSUM), Generalized Likelihood Ratio Test (GLRT), and Shiryayev-Roberts (S-R) charts for a given $$ARL_0$$ A R L 0 . Additionally, we propose hard-threshold and soft-threshold EWMA charts for detecting changes characterized by sparse signals, where the change occurs in only a few components. Comparative analyses, including adaptive techniques, demonstrate the robust performance and straightforward design of the EWMA procedure, making it a recommended choice. The detection of mean changes in daily returns for Dow Jones industrial stock prices is used for illustration.

Keywords: Stationary average delay detection time; Change point; EWMA procedure; MA procedure; Generalized LRT; Primary 62L10; Secondary 62N15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10155-9

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