Control charts for high-dimensional time series with estimated in-control parameters

REFERENCES

• Albers, W., and W. C. Kallenberg. 2004. “Are Estimated Control Charts in Control?” Statistics 38 (1): 67–79. https://doi.org/10.1080/02669760310001619369
   Web of Science ®Google Scholar
• Alwan, L. C., and H. V. Roberts. 1988. “Time-Series Modeling for Statistical Process Control.” Journal of Business & Economic Statistics 6 (1): 87–95.
   Web of Science ®Google Scholar
• Andersson, E., D. Bock, and M. Frisén. 2004. “Detection of Turning Points in Business Cycles.” Journal of Business Cycle Measurement and Analysis 2004 (1): 93–108. https://doi.org/10.1787/jbcma-v2004-art6-en
   Google Scholar
• Bai, Z., and J. W. Silverstein. 2010. Spectral Analysis of Large Dimensional Random Matrices, Vol. 20. New York: Springer.
   Google Scholar
• Bodnar, O. 2007. “Sequential Procedures for Monitoring Covariances of Asset Returns.” In Advances in Risk Management, edited by G. N. Gregoriou, 241–64. New York: Palgrave.
   Google Scholar
• Bodnar, O. 2009a. “Application of the Generalized Likelihood Ratio Test for Detecting Changes in the Mean of Multivariate Garch Processes.” Communications in Statistics - Simulation and Computation 38 (5): 919–938. https://doi.org/10.1080/03610910802691861
   Web of Science ®Google Scholar
• Bodnar, O. 2009b. “Sequential Surveillance of the Tangency Portfolio Weights.” International Journal of Theoretical and Applied Finance 12 (06): 797–810. https://doi.org/10.1142/S0219024909005464
   Google Scholar
• Bodnar, O., and W. Schmid. 2007. “Surveillance of the Mean Behavior of Multivariate Time Series.” Statistica Neerlandica 61 (4): 383–406. https://doi.org/10.1111/j.1467-9574.2007.00365.x
   Web of Science ®Google Scholar
• Bodnar, O., and W. Schmid. 2011. “CUSUM Charts for Monitoring the Mean of a Multivariate Gaussian Process.” Journal of Statistical Planning and Inference 141 (6): 2055–2070. https://doi.org/10.1016/j.jspi.2010.12.020
   Web of Science ®Google Scholar
• Bodnar, O., and W. Schmid. 2017. “CUSUM Control Schemes for Monitoring the Covariance Matrix of Multivariate Time Series.” Statistics 51 (4): 722–744. https://doi.org/10.1080/02331888.2016.1268616
   Web of Science ®Google Scholar
• Bodnar, R., T. Bodnar, and W. Schmid. 2023. “Sequential Monitoring of High-Dimensional Time Series.” Scandinavian Journal of Statistics 50 (3): 962–992. https://doi.org/10.1111/sjos.12607
   Web of Science ®Google Scholar
• Bodnar, T., H. Dette, and N. Parolya. 2019. “Testing for Independence of Large Dimensional Vectors.” The Annals of Statistics 47 (5): 2977–3008. https://doi.org/10.1214/18-AOS1771
   Web of Science ®Google Scholar
• Brockwell, P. J., and R. A. Davis. 1991. Time Series: Theory and Methods. New York: Springer Science & Business Media.
   Google Scholar
• Chen, S., and H. B. Nembhard. 2011. “A High-Dimensional Control Chart for Profile Monitoring.” Quality and Reliability Engineering International 27 (4): 451–464. https://doi.org/10.1002/qre.1140
   Web of Science ®Google Scholar
• Crosier, R. 1988. “Multivariate Generalizations of Cumulative Sum Quality-Control Schemes.” Technometrics 30 (3): 291–303. https://doi.org/10.1080/00401706.1988.10488402
   Web of Science ®Google Scholar
• Frisén, M. 1992. “Evaluations of Methods for Statistical Surveillance.” Statistics in Medicine 11 (11): 1489–1502. https://doi.org/10.1002/sim.4780111107
   PubMed Web of Science ®Google Scholar
• Golosnoy, V., and W. Schmid. 2007. “EWMA Control Charts for Monitoring Optimal Portfolio Weights.” Sequential Analysis 26 (2): 195–224. https://doi.org/10.1080/07474940701247099
   Google Scholar
• Golosnoy, W., I. Okhrin, S. Ragulin, and W. Schmid. 2011. “On the Application of SPC in Finance.” Frontiers in Statistical Quality Control 9: 119–32.
   Google Scholar
• Hamilton, J. D. 1994. Time Series Analysis. New Jersey: Princeton University Press.
   Google Scholar
• Harville, D. A. 1997. Matrix Algebra from Statistician’s Perspective. New York: Springer.
   Google Scholar
• Hotelling, H. 1947. “Multivariate Quality Control—Illustrated by the Air Testing of Sample Bombsights.” In Techniques of Statistical Analysis, edited by C. Eisenhart, M. W. Hastay, and W. Wallis, 111–184. New York: McGraw Hill.
   Google Scholar
• Jardim, F. S., S. Chakraborti, and E. K. Epprecht. 2020. “Two Perspectives for Designing a Phase II Control Chart with Estimated Parameters: The Case of the Shewhart X Chart.” Journal of Quality Technology 52 (2): 198–217. https://doi.org/10.1080/00224065.2019.1571345
   Web of Science ®Google Scholar
• Jensen, W. A., L. A. Jones-Farmer, C. W. Champ, and W. H. Woodall. 2006. “Effects of Parameter Estimation on Control Chart Properties: A Literature Review.” Journal of Quality Technology 38 (4): 349–364. https://doi.org/10.1080/00224065.2006.11918623
   Web of Science ®Google Scholar
• Knoth, S. 2021. “Steady-State Average Run Length (s): Methodology, Formulas, and Numerics.” Sequential Analysis 40 (3): 405–426. https://doi.org/10.1080/07474946.2021.1940501
   Web of Science ®Google Scholar
• Knoth, S., and W. Schmid. 2002. “Monitoring the Mean and the Variance of a Stationary Process.” Statistica Neerlandica 56 (1): 77–100. https://doi.org/10.1111/1467-9574.03000
   Web of Science ®Google Scholar
• Kramer, H., and W. Schmid. 1997. “EWMA Charts for Multivariate Time Series.” Sequential Analysis 16 (2): 131–154. https://doi.org/10.1080/07474949708836378
   Google Scholar
• Kramer, H., and W. Schmid. 2000. “The Influence of Parameter Estimation on the ARL of Shewhart Type Charts for Time Series.” Statistical Papers 41 (2): 173–196. https://doi.org/10.1007/BF02926102
   Web of Science ®Google Scholar
• Lawson, A., and K. Kleinman. 2005. Spatial & Syndromic Surveillance. New York: Wiley.
   Google Scholar
• Lax, P. D. 2007. Linear Algebra and Its Applications, Vol. 78. New Jersey: John Wiley & Sons.
   Google Scholar
• Li, Y., Y. Liu, C. Zou, and W. Jiang. 2014. “A Self-Starting Control Chart for High-Dimensional Short-Run Processes.” International Journal of Production Research 52 (2): 445–461. https://doi.org/10.1080/00207543.2013.832001
   Web of Science ®Google Scholar
• Lowry, C., W. Woodall, C. Champ, and S. Rigdon. 1992. “A Multivariate Exponentially Weighted Moving Average Control Chart.” Technometrics 34 (1): 46–53. https://doi.org/10.2307/1269551
   Web of Science ®Google Scholar
• Lütkepohl, H. 2005. New Introduction to Multiple Time Series Analysis. Berlin: Springer Science & Business Media.
   Google Scholar
• Mathai, A. M., and S. B. Provost. 1992. Quadratic Forms in Random Variables: Theory and Applications. New York: Dekker.
   Google Scholar
• Messaoud, A., C. Weihs, and F. Hering. 2008. “Detection of Chatter Vibration in a Drilling Process Using Multivariate Control Charts.” Computational Statistics & Data Analysis 52 (6): 3208–3219. https://doi.org/10.1016/j.csda.2007.09.029
   Web of Science ®Google Scholar
• Montgomery, D. C. 2020. Introduction to Statistical Quality Control. Hoboken: John Wiley & Sons.
   Google Scholar
• Muirhead, R. J. 1982. Aspects of Multivariate Statistical Theory. New York: Wiley.
   Google Scholar
• Ngai, H., and J. Zhang. 2001. “Multivariate Cumulative Sum Control Charts Based on Projection Pursuit.” Statistica Sinica 11: 747–766.
   Web of Science ®Google Scholar
• Otto, P., and W. Schmid. 2023. “A General Framework for Spatial Garch Models.” Statistical Papers 64 (5): 1721–1747. https://doi.org/10.1007/s00362-022-01357-1
   Web of Science ®Google Scholar
• Page, E. S. 1954. “Continuous Inspection Schemes.” Biometrika 41 (1-2): 100–115. https://doi.org/10.1093/biomet/41.1-2.100
   Web of Science ®Google Scholar
• Pignatiello, J., and G. Runger. 1990. “Comparisons of Multivariate CUSUM Charts.” Journal of Quality Technology 22 (3): 173–186. https://doi.org/10.1080/00224065.1990.11979237
   Web of Science ®Google Scholar
• Qiu, P. 2013. Introduction to Statistical Process Control. Boca Raton, FL: CRC press.
   Google Scholar
• Reinsel, G. 1993. Multivariate Time Series Analysis. New York: John Wiley & Sons.
   Google Scholar
• Roberts, S. 1959. “Control Chart Tests Based on Geometric Moving Averages.” Technometrics 1 (3): 239–250. https://doi.org/10.1080/00401706.1959.10489860
   Google Scholar
• Saleh, N. A., M. A. Mahmoud, L. A. Jones-Farmer, I. Zwetsloot, and W. H. Woodall. 2015. “Another Look at the EWMA Control Chart with Estimated Parameters.” Journal of Quality Technology 47 (4): 363–382. https://doi.org/10.1080/00224065.2015.11918140
   Web of Science ®Google Scholar
• Sarmiento, M. G., F. S. Jardim, S. Chakraborti, and E. K. Epprecht. 2022. “Design of Variance Control Charts with Estimated Parameters: A Head to Head Comparison between Two Perspectives.” Journal of Quality Technology 54 (3): 249–268. https://doi.org/10.1080/00224065.2020.1834892
   Web of Science ®Google Scholar
• Schipper, S., and W. Schmid. 2001. “Sequential Methods for Detecting Changes in the Variance of Economic Time Series.” Sequential Analysis 20 (4): 235–262. https://doi.org/10.1081/SQA-100107647
   Google Scholar
• Schmid, W. 1995. “On the Run Length of a Shewhart Chart for Correlated Data.” Statistical Papers 36 (1): 111–130. https://doi.org/10.1007/BF02926025
   Web of Science ®Google Scholar
• Schmid, W. 1997a. “CUSUM Control Schemes for Gaussian Processes.” Statistical Papers 38 (2): 191–217. https://doi.org/10.1007/BF02925223
   Web of Science ®Google Scholar
• Schmid, W. 1997b. “On EWMA Charts for Time Series.” In Frontiers in Statistical Quality Control, edited by Hans-Joachim Lenz, Peter-Theodor Wilrich, 115–137. Berlin, Heidelberg: Springer.
   Google Scholar
• Schmid, W., and A. Schöne. 1997. “Some Properties of the EWMA Control Chart in the Presence of Autocorrelation.” The Annals of Statistics 25 (3): 1277–1283. https://doi.org/10.1214/aos/1069362748
   Web of Science ®Google Scholar
• Schmid, W., and D. Tzotchev. 2004. “Statistical Surveillance of the Parameters of a One-Factor Cox-Ingersoll-Ross Model.” Sequential Analysis 23 (3): 379–412. https://doi.org/10.1081/SQA-200027052
   Google Scholar
• Severin, T., and W. Schmid. 1999. “Monitoring Changes in GARCH Models.” Allgemeines Statistisches Archiv (AStA) 83: 281–307.
   Google Scholar
• Shewhart, W. A. 1926. “Quality Control Charts.” Bell System Technical Journal 5 (4): 593–603. https://doi.org/10.1002/j.1538-7305.1926.tb00125.x
   Google Scholar
• Śliwa, P., and W. Schmid. 2005. “Monitoring the Cross-Covariances of a Multivariate Time Series.” Metrika 61 (1): 89–115. https://doi.org/10.1007/s001840400326
   Web of Science ®Google Scholar
• Sonesson, C., and D. Bock. 2003. “A Review and Discussion of Prospective Statistical Surveillance in Public Health.” Journal of the Royal Statistical Society Series A: Statistics in Society 166 (1): 5–21. https://doi.org/10.1111/1467-985X.00256
   Web of Science ®Google Scholar
• Theodossiou, P. T. 1993. “Predicting Shifts in the Mean of a Multivariate Time Series Process: An Application in Predicting Business Failures.” Journal of the American Statistical Association 88 (422): 441–449. https://doi.org/10.1080/01621459.1993.10476294
   Web of Science ®Google Scholar
• Wang, K., and W. Jiang. 2009. “High-Dimensional Process Monitoring and Fault Isolation via Variable Selection.” Journal of Quality Technology 41 (3): 247–258. https://doi.org/10.1080/00224065.2009.11917780
   Web of Science ®Google Scholar
• Wang, Z., Y. Li, and X. Zhou. 2017. “A Statistical Control Chart for Monitoring High-Dimensional Poisson Data Streams.” Quality and Reliability Engineering International 33 (2): 307–321. https://doi.org/10.1002/qre.2005
   Web of Science ®Google Scholar