IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v50y2023i3p962-992.html
   My bibliography  Save this article

Sequential monitoring of high‐dimensional time series

Author

Listed:
  • Rostyslav Bodnar
  • Taras Bodnar
  • Wolfgang Schmid

Abstract

In the paper we derive new types of multivariate exponentially weighted moving average (EWMA) control charts which are based on the Euclidean distance and on the distance defined by using the inverse of the diagonal matrix consisting of the variances. The design of the proposed control schemes does not involve the computation of the inverse covariance matrix and, thus, it can be used in the high‐dimensional setting. The distributional properties of the control statistics are obtained and are used in the determination of the new control procedures. Within an extensive simulation study, the new approaches are compared with the multivariate EWMA control charts which are based on the Mahalanobis distance.

Suggested Citation

  • Rostyslav Bodnar & Taras Bodnar & Wolfgang Schmid, 2023. "Sequential monitoring of high‐dimensional time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 962-992, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:962-992
    DOI: 10.1111/sjos.12607
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12607
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12607?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Alexander Aue & Lajos Horváth & Daniel F. Pellatt, 2017. "Functional Generalized Autoregressive Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 3-21, January.
    2. Gupta, Abhimanyu & Robinson, Peter M., 2018. "Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension," Journal of Econometrics, Elsevier, vol. 202(1), pages 92-107.
    3. Bodnar, Taras & Reiß, Markus, 2016. "Exact and asymptotic tests on a factor model in low and large dimensions with applications," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 125-151.
    4. Olha Bodnar & Wolfgang Schmid, 2007. "Surveillance of the mean behavior of multivariate time series," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 383-406, November.
    5. Alexander Chudik & M. Hashem Pesaran, 2013. "Econometric Analysis of High Dimensional VARs Featuring a Dominant Unit," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 592-649, August.
    6. Bodnar, Taras & Gupta, Arjun K. & Parolya, Nestor, 2016. "Direct shrinkage estimation of large dimensional precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 223-236.
    7. Gupta, Abhimanyu & Robinson, Peter M., 2015. "Inference on higher-order spatial autoregressive models with increasingly many parameters," Journal of Econometrics, Elsevier, vol. 186(1), pages 19-31.
    8. Christian Sonesson & David Bock, 2003. "A review and discussion of prospective statistical surveillance in public health," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 166(1), pages 5-21, February.
    9. Linus Schiöler & Marianne Fris�n, 2012. "Multivariate outbreak detection," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 223-242, April.
    10. Eva Andersson & David Bock & Marianne Frisén, 2004. "Detection of Turning Points in Business Cycles," Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2004(1), pages 93-108.
    11. Messaoud, Amor & Weihs, Claus & Hering, Franz, 2008. "Detection of chatter vibration in a drilling process using multivariate control charts," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3208-3219, February.
    12. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    13. Dias, Gustavo Fruet & Kapetanios, George, 2018. "Estimation and forecasting in vector autoregressive moving average models for rich datasets," Journal of Econometrics, Elsevier, vol. 202(1), pages 75-91.
    14. Meyer, Sebastian & Held, Leonhard & Höhle, Michael, 2017. "Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 77(i11).
    15. Olha Bodnar, 2009. "Sequential Surveillance Of The Tangency Portfolio Weights," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 797-810.
    16. Dette, Holger & Dörnemann, Nina, 2020. "Likelihood ratio tests for many groups in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    17. Lam, Clifford & Yao, Qiwei, 2012. "Factor modeling for high-dimensional time series: inference for the number of factors," LSE Research Online Documents on Economics 45684, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Bodnar, Olha & Bodnar, Taras & Okhrin, Yarema, 2009. "Surveillance of the covariance matrix based on the properties of the singular Wishart distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3372-3385, July.
    3. Bock, David & Pettersson, Kjell, 2007. "Explorative analysis of spatial aspects on the Swedish influenza data," Research Reports 2007:10, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    4. Matteo Barigozzi & Marc Hallin, 2017. "A network analysis of the volatility of high dimensional financial series," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(3), pages 581-605, April.
    5. Bodnar, Taras & Mazur, Stepan & Ngailo, Edward & Parolya, Nestor, 2017. "Discriminant analysis in small and large dimensions," Working Papers 2017:6, Örebro University, School of Business.
    6. Mårten Gulliksson & Stepan Mazur, 2020. "An Iterative Approach to Ill-Conditioned Optimal Portfolio Selection," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 773-794, December.
    7. Gupta, Abhimanyu, 2023. "Efficient closed-form estimation of large spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 148-167.
    8. Taras Bodnar & Holger Dette & Nestor Parolya & Erik Thors'en, 2019. "Sampling Distributions of Optimal Portfolio Weights and Characteristics in Low and Large Dimensions," Papers 1908.04243, arXiv.org, revised Apr 2023.
    9. Ayden Higgins & Federico Martellosio, 2019. "Shrinkage Estimation of Network Spillovers with Factor Structured Errors," Papers 1909.02823, arXiv.org, revised Nov 2021.
    10. Matteo Barigozzi & Marc Hallin, 2015. "Networks, Dynamic Factors, and the Volatility Analysis of High-Dimensional Financial Series," Papers 1510.05118, arXiv.org, revised Jul 2016.
    11. Marc Hallin & Gilles Nisol & Shahin Tavakoli, 2023. "Factor models for high‐dimensional functional time series I: Representation results," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(5-6), pages 578-600, September.
    12. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    13. Bock, David, 2007. "Evaluations of likelihood based surveillance of volatility," Research Reports 2007:9, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    14. Abhimanyu Gupta & Xi Qu, 2021. "Consistent specification testing under spatial dependence," Papers 2101.10255, arXiv.org, revised Aug 2022.
    15. Gupta, Abhimanyu, 2018. "Nonparametric specification testing via the trinity of tests," Journal of Econometrics, Elsevier, vol. 203(1), pages 169-185.
    16. Marianne Frisén, 2014. "Spatial outbreak detection based on inference principles for multivariate surveillance," IISE Transactions, Taylor & Francis Journals, vol. 46(8), pages 759-769, August.
    17. Michaelides, Alexander & Kokas, Sotirios & Gupta, Abhimanyu, 2017. "Credit Market Spillovers: Evidence from a Syndicated Loan Market Network," CEPR Discussion Papers 12424, C.E.P.R. Discussion Papers.
    18. Christian Brownlees & Gu{dh}mundur Stef'an Gu{dh}mundsson & Yaping Wang, 2024. "Performance of Empirical Risk Minimization For Principal Component Regression," Papers 2409.03606, arXiv.org, revised Sep 2024.
    19. Taras Bodnar & Solomiia Dmytriv & Yarema Okhrin & Nestor Parolya & Wolfgang Schmid, 2020. "Statistical inference for the EU portfolio in high dimensions," Papers 2005.04761, arXiv.org.
    20. Bock, David & Andersson, Eva & Frisén, Marianne, 2007. "Statistical Surveillance of Epidemics: Peak Detection of Influenza in Sweden," Research Reports 2007:6, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:962-992. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.