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Optimal Multivariate EWMA Chart for Detecting Common Change in Mean

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  • Yanhong Wu

    (California State University Stanislaus)

  • Wei Biao Wu

    (University of Chicago)

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.

Suggested Citation

  • Yanhong Wu & Wei Biao Wu, 2025. "Optimal Multivariate EWMA Chart for Detecting Common Change in Mean," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-22, June.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10155-9
    DOI: 10.1007/s11009-025-10155-9
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    References listed on IDEAS

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    1. Bai, Jushan, 2010. "Common breaks in means and variances for panel data," Journal of Econometrics, Elsevier, vol. 157(1), pages 78-92, July.
    2. Zou, Changliang & Qiu, Peihua, 2009. "Multivariate Statistical Process Control Using LASSO," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1586-1596.
    3. Dukpa Kim, 2014. "Common breaks in time trends for large panel data with a factor structure," Econometrics Journal, Royal Economic Society, vol. 17(3), pages 301-337, October.
    4. Y. Mei, 2010. "Efficient scalable schemes for monitoring a large number of data streams," Biometrika, Biometrika Trust, vol. 97(2), pages 419-433.
    5. Nishimura, Kazuya & Matsuura, Shun & Suzuki, Hideo, 2015. "Multivariate EWMA control chart based on a variable selection using AIC for multivariate statistical process monitoring," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 7-13.
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