IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v85y2023i1d10.1007_s13171-021-00251-6.html
   My bibliography  Save this article

Estimation and Testing in Multivariate Generalized Ornstein-Uhlenbeck Processes with Change-Points

Author

Listed:
  • Sévérien Nkurunziza

    (University of Windsor)

Abstract

In this paper, we consider an inference problem about the drift parameter matrix of multivariate generalized Ornstein-Uhlenbeck processes with multiple unknown change-points in the case where the drift parameter matrix is suspected to satisfy some restrictions. The established results generalize in six ways some recent findings about univariate generalized Ornstein-Uhlenbeck processes. First, we consider a multivariate process with multiple change-points. Second, we weaken the assumptions underlying some recent findings and we derive the unrestricted estimator (UE) and the restricted estimator (RE). Third, we derive the asymptotic property of the UE and the RE. Fourth, we construct a test for testing the hypothesized constraint. Fifth, we establish the asymptotic power of the derived test and we prove that it is consistent. Sixth, we derive a class of shrinkage estimators (SEs) and its asymptotic distributional risk.

Suggested Citation

  • Sévérien Nkurunziza, 2023. "Estimation and Testing in Multivariate Generalized Ornstein-Uhlenbeck Processes with Change-Points," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 351-400, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00251-6
    DOI: 10.1007/s13171-021-00251-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-021-00251-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-021-00251-6?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sévérien Nkurunziza, 2013. "Extension of some important identities in shrinkage-pretest strategies," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 937-947, October.
    2. Fuqi Chen & Sévérien Nkurunziza, 2016. "A class of Stein-rules in multivariate regression model with structural changes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 83-102, March.
    3. Fuqi Chen & Rogemar Mamon & Sévérien Nkurunziza, 2018. "Inference for a change-point problem under a generalised Ornstein–Uhlenbeck setting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 807-853, August.
    4. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    5. Sévérien Nkurunziza & Pei Patrick Zhang, 2018. "Estimation and testing in generalized mean-reverting processes with change-point," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 191-215, April.
    6. Herold Dehling & Brice Franke & Thomas Kott & Reg Kulperger, 2014. "Change point testing for the drift parameters of a periodic mean reversion process," Statistical Inference for Stochastic Processes, Springer, vol. 17(1), pages 1-18, April.
    7. Herold Dehling & Brice Franke & Thomas Kott, 2010. "Drift estimation for a periodic mean reversion process," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 175-192, October.
    8. Sévérien Nkurunziza & Lei Shen, 2020. "Inference in a multivariate generalized mean-reverting process with a change-point," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 199-226, April.
    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. Sévérien Nkurunziza & Lei Shen, 2020. "Inference in a multivariate generalized mean-reverting process with a change-point," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 199-226, April.
    2. Fuqi Chen & Rogemar Mamon & Sévérien Nkurunziza, 2018. "Inference for a change-point problem under a generalised Ornstein–Uhlenbeck setting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 807-853, August.
    3. Yunhong Lyu & Sévérien Nkurunziza, 2023. "Inference in generalized exponential O–U processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 581-618, October.
    4. Sévérien Nkurunziza & Pei Patrick Zhang, 2018. "Estimation and testing in generalized mean-reverting processes with change-point," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 191-215, April.
    5. Koo, Bonsoo & Seo, Myung Hwan, 2015. "Structural-break models under mis-specification: Implications for forecasting," Journal of Econometrics, Elsevier, vol. 188(1), pages 166-181.
    6. Boldea, Otilia & Hall, Alastair R., 2013. "Estimation and inference in unstable nonlinear least squares models," Journal of Econometrics, Elsevier, vol. 172(1), pages 158-167.
    7. Alastair R. Hall & Denise R. Osborn & Nikolaos Sakkas, 2017. "The asymptotic behaviour of the residual sum of squares in models with multiple break points," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 667-698, October.
    8. Molly C. Klanderman & Kathryn B. Newhart & Tzahi Y. Cath & Amanda S. Hering, 2020. "Fault isolation for a complex decentralized waste water treatment facility," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 931-951, August.
    9. Mohitosh Kejriwal & Xuewen Yu & Pierre Perron, 2020. "Bootstrap procedures for detecting multiple persistence shifts in heteroskedastic time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 676-690, September.
    10. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2012. "Inference regarding multiple structural changes in linear models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 281-302.
    11. Pierre Perron & Yohei Yamamoto & Jing Zhou, 2020. "Testing jointly for structural changes in the error variance and coefficients of a linear regression model," Quantitative Economics, Econometric Society, vol. 11(3), pages 1019-1057, July.
    12. Luis Garicano & Claire Lelarge & John Van Reenen, 2016. "Firm Size Distortions and the Productivity Distribution: Evidence from France," American Economic Review, American Economic Association, vol. 106(11), pages 3439-3479, November.
    13. Liao, Huei-Chu & Lee, Yi-Huey & Suen, Yu-Bo, 2008. "Electronic trading system and returns volatility in the oil futures market," Energy Economics, Elsevier, vol. 30(5), pages 2636-2644, September.
    14. Mohitosh Kejriwal, 2020. "A Robust Sequential Procedure for Estimating the Number of Structural Changes in Persistence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(3), pages 669-685, June.
    15. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2008. "Inference regarding multiple structural changes in linear models estimated via two stage least squares," MPRA Paper 9251, University Library of Munich, Germany, revised 20 Jun 2008.
    16. Rachid Belfadli & Khalifa Es-Sebaiy & Fatima-Ezzahra Farah, 2022. "Statistical analysis of the non-ergodic fractional Ornstein–Uhlenbeck process with periodic mean," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 885-911, October.
    17. Petrenko, Victoria (Петренко, ВИктория) & Skrobotov, Anton (Скроботов, Антон) & Turuntseva, Maria (Турунцева, Мария), 2016. "Testing of Changes in Persistence and Their Effect on the Forecasting Quality [Тестирование Изменения Инерционности И Влияние На Качество Прогнозов]," Working Papers 542, Russian Presidential Academy of National Economy and Public Administration.
    18. Chen Fuqi & Nkurunziza Sévérien, 2014. "Constrained inference in multiple regression with structural changes," Statistics & Risk Modeling, De Gruyter, vol. 31(3-4), pages 1-21, December.
    19. Oka, Tatsushi & Perron, Pierre, 2018. "Testing for common breaks in a multiple equations system," Journal of Econometrics, Elsevier, vol. 204(1), pages 66-85.
    20. Yohei Yamamoto & Pierre Perron, 2013. "Estimating and testing multiple structural changes in linear models using band spectral regressions," Econometrics Journal, Royal Economic Society, vol. 16(3), pages 400-429, October.

    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:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00251-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.