skip to main content
10.1145/3686592.3686597acmotherconferencesArticle/Chapter ViewAbstractPublication PagesicomsConference Proceedingsconference-collections
research-article

Robust Covariance Matrix Estimator with Change Points for Multivariate Jump Diffusion Process

Published: 02 December 2024 Publication History

Abstract

We propose a method for constructing covariance matrix estimators robust to abrupt and persistent changes in the underlying spot covariance of a multivariate jump-diffusion process. We take the consistent estimator of the increments of the integrated covariance process and rebuild them as a group of co-occurring signals. We then construct ℓ1-regularized versions using the group LASSO method to detect co-occurring changes in these signals. The group LASSO method is computationally efficient and uses reduced dynamic programming to eliminate spurious change points. The algorithm is computationally fast and accurately identifies the structural common change points in the underlying integrated covariance matrix increments. We empirically demonstrate that the proposed estimator outperforms the benchmark estimators in various forecasting metrics, using different training windows and data frequencies.

References

[1]
Yacine Aït-Sahalia, Jianqing Fan, and Dacheng Xiu. 2010. High-frequency covariance estimates with noisy and asynchronous financial data. J. Amer. Statist. Assoc. 105, 492 (2010), 1504–1517.
[2]
Torben G Andersen, Tim Bollerslev, Francis X Diebold, and Paul Labys. 2003. Modeling and forecasting realized volatility. Econometrica 71, 2 (2003), 579–625.
[3]
Alexander Aue and Lajos Horváth. 2013. Structural breaks in time series. Journal of Time Series Analysis 34, 1 (2013), 1–16.
[4]
Valeriy Avanesov and Nazar Buzun. 2018. Change-point detection in high-dimensional covariance structure. Electronic Journal of Statistics 12, 2 (2018), 3254–3294.
[5]
Greeshma Balabhadra, El Mehdi Ainasse, and Pawel Polak. 2023. High-Frequency Volatility Estimation with Fast Multiple Change Points Detection. arXiv preprint arXiv:2303.10550 (2023).
[6]
Ole E. Barndorff-Nielsen and Neil Shephard. 2004. Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics. Econometrica 72, 3 (2004), 885–925.
[7]
Ole E Barndorff-Nielsen and Neil Shephard. 2004. Measuring the impact of jumps in multivariate price processes using bipower covariation. Technical Report. Discussion paper, Nuffield College, Oxford University.
[8]
Ole E. Barndorff-Nielsen and Neil Shephard. 2004. Power and bipower variation with stochastic volatility and jumps. Journal of Financial Econometrics 2 (2004), 1–48.
[9]
Jérémie Bigot, Rolando J Biscay, Jean-Michel Loubes, and Lillian Muñiz-Alvarez. 2011. Group lasso estimation of high-dimensional covariance matrices. The Journal of Machine Learning Research 12 (2011), 3187–3225.
[10]
Kevin Bleakley and Jean-Philippe Vert. 2011. The group fused Lasso for multiple change-point detection. (June 2011). working paper or preprint.
[11]
Tim Bollerslev, Jia Li, Andrew J Patton, and Rogier Quaedvlieg. 2020. Realized semicovariances. Econometrica 88, 4 (2020), 1515–1551.
[12]
Roxana Chiriac and Valeri Voev. 2011. Modelling and forecasting multivariate realized volatility. Journal of Applied Econometrics 26, 6 (2011), 922–947.
[13]
Holger Dette, Guangming Pan, and Qing Yang. 2022. Estimating a change point in a sequence of very high-dimensional covariance matrices. J. Amer. Statist. Assoc. 117, 537 (2022), 444–454.
[14]
Z. Harchaoui and C. Lévy-Leduc. 2010. Multiple Change-Point Estimation With a Total Variation Penalty. J. Amer. Statist. Assoc. 105, 492 (2010), 1480–1493.
[15]
Wolfgang Härdle, Helmut Herwartz, and Vladimir Spokoiny. 2003. Time inhomogeneous multiple volatility modeling. Journal of Financial econometrics 1, 1 (2003), 55–95.
[16]
Céline Levy-Leduc and Zaid Harchaoui. 2008. Catching Change-points with Lasso. In Advances in Neural Information Processing Systems, Vol. 20. Curran Associates Inc., Red Hook, NY, USA, 617–624.
[17]
Yifan Li and Ingmar Nolte. 2016. High-Frequency Volatility Modelling: A Markov-Switching Autoregressive Conditional Intensity Model. SSRN Electronic Journal (01 2016).
[18]
Yu-Ning Li, Degui Li, and Piotr Fryzlewicz. 2022. Detection of multiple structural breaks in large covariance matrices. Journal of Business & Economic Statistics 41, 3 (2022), 1–43.
[19]
Jean-Philippe Vert and Kevin Bleakley. 2010. Fast detection of multiple change-points shared by many signals using group LARS. Advances in neural information processing systems 23 (2010).
[20]
Ines Wilms and Christophe Croux. 2018. An algorithm for the multivariate group lasso with covariance estimation. Journal of Applied Statistics 45, 4 (2018), 668–681.

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Other conferences
ICoMS '24: Proceedings of the 2024 7th International Conference on Mathematics and Statistics
June 2024
134 pages
ISBN:9798400707223
DOI:10.1145/3686592
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 02 December 2024

Check for updates

Author Tags

  1. Covariance
  2. Group fused LASSO
  3. High-Frequency
  4. Change points

Qualifiers

  • Research-article

Conference

ICoMS 2024

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • 0
    Total Citations
  • 11
    Total Downloads
  • Downloads (Last 12 months)11
  • Downloads (Last 6 weeks)3
Reflects downloads up to 10 Feb 2025

Other Metrics

Citations

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Full Text

View this article in Full Text.

Full Text

HTML Format

View this article in HTML Format.

HTML Format

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media