IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v128y2018i11p3679-3723.html
   My bibliography  Save this article

Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes

Author

Listed:
  • Hoffmann, Michael
  • Vetter, Mathias
  • Dette, Holger

Abstract

In applications the properties of a stochastic feature often change gradually rather than abruptly, that is: after a constant phase for some time they slowly start to vary. In this paper we discuss statistical inference for the detection and the localization of gradual changes in the jump characteristic of a discretely observed Ito semimartingale. We propose a new measure of time variation for the jump behaviour of the process. The statistical uncertainty of a corresponding estimate is analysed by deriving new results on the weak convergence of a sequential empirical tail integral process and a corresponding multiplier bootstrap procedure.

Suggested Citation

  • Hoffmann, Michael & Vetter, Mathias & Dette, Holger, 2018. "Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3679-3723.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:11:p:3679-3723
    DOI: 10.1016/j.spa.2017.12.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414917303113
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2017.12.005?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. Kosorok, Michael R., 2003. "Bootstraps of sums of independent but not identically distributed stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 299-318, February.
    2. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    3. A. F. Bissell, 1984. "The Performance of Control Charts and Cusums Under Linear Trend," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 145-151, June.
    4. Figueroa-López, José E. & Houdré, Christian, 2009. "Small-time expansions for the transition distributions of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3862-3889, November.
    5. Hoffmann, Michael & Vetter, Mathias, 2017. "Weak convergence of the empirical truncated distribution function of the Lévy measure of an Itō semimartingale," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1517-1543.
    6. Aue, Alexander & Steinebach, Josef, 2002. "A note on estimating the change-point of a gradually changing stochastic process," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 177-191, January.
    7. Hušková M. & Steinebach J., 2002. "Asymptotic Tests For Gradual Changes," Statistics & Risk Modeling, De Gruyter, vol. 20(1-4), pages 137-152, April.
    8. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marie Hušková & Zuzana Prášková & Josef G. Steinebach, 2022. "Estimating a gradual parameter change in an AR(1)-process," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 771-808, October.

    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. Chen, Zhanshou & Xu, Qiongyao & Li, Huini, 2019. "Inference for multiple change points in heavy-tailed time series via rank likelihood ratio scan statistics," Economics Letters, Elsevier, vol. 179(C), pages 53-56.
    2. Stergios B. Fotopoulos & Abhishek Kaul & Vasileios Pavlopoulos & Venkata K. Jandhyala, 2024. "Adaptive parametric change point inference under covariance structure changes," Statistical Papers, Springer, vol. 65(5), pages 2887-2913, July.
    3. Woody, Jonathan & Lund, Robert, 2014. "A linear regression model with persistent level shifts: An alternative to infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 118-124.
    4. Jean-François Quessy, 2019. "Consistent nonparametric tests for detecting gradual changes in the marginals and the copula of multivariate time series," Statistical Papers, Springer, vol. 60(3), pages 717-746, June.
    5. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    6. Lijing Ma & Andrew J. Grant & Georgy Sofronov, 2020. "Multiple change point detection and validation in autoregressive time series data," Statistical Papers, Springer, vol. 61(4), pages 1507-1528, August.
    7. Pedro Galeano & Dominik Wied, 2017. "Dating multiple change points in the correlation matrix," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 331-352, June.
    8. Marie Hušková & Zuzana Prášková & Josef G. Steinebach, 2022. "Estimating a gradual parameter change in an AR(1)-process," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 771-808, October.
    9. Yunwei Cui & Rongning Wu & Qi Zheng, 2021. "Estimation of change‐point for a class of count time series models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1277-1313, December.
    10. Michael Messer, 2022. "Bivariate change point detection: Joint detection of changes in expectation and variance," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 886-916, June.
    11. Lee, Taewook & Baek, Changryong, 2020. "Block wild bootstrap-based CUSUM tests robust to high persistence and misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    12. Holger Dette & Dominik Wied, 2016. "Detecting relevant changes in time series models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 371-394, March.
    13. Castrillón-Candás, Julio E. & Kon, Mark, 2022. "Anomaly detection: A functional analysis perspective," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    14. Shi, Xuesheng & Gallagher, Colin & Lund, Robert & Killick, Rebecca, 2022. "A comparison of single and multiple changepoint techniques for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    15. Woody, Jonathan, 2015. "Time series regression with persistent level shifts," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 22-29.
    16. Bouzebda, Salim & Ferfache, Anouar Abdeldjaoued, 2023. "Asymptotic properties of semiparametric M-estimators with multiple change points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    17. Skrobotov, Anton, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    18. Michael Messer & Stefan Albert & Gaby Schneider, 2018. "The multiple filter test for change point detection in time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(6), pages 589-607, August.
    19. Reiß, Markus, 2013. "Testing the characteristics of a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2808-2828.
    20. Daniela Jarušková, 2015. "Detecting non-simultaneous changes in means of vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 681-700, December.

    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:eee:spapps:v:128:y:2018:i:11:p:3679-3723. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.