IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v48y2021i2p429-455.html
   My bibliography  Save this article

On inference for modes under long memory

Author

Listed:
  • Jan Beran
  • Klaus Telkmann

Abstract

We consider inference for local maxima of the marginal density function of strongly dependent linear processes. Weak consistency of the estimated modular set and the number of modes is derived. A uniform reduction principle for kernel density estimators is used to obtain confidence sets for the set of modes. The results can be extended to multivariate modes. Simulations illustrate the asymptotic results.

Suggested Citation

  • Jan Beran & Klaus Telkmann, 2021. "On inference for modes under long memory," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 429-455, June.
  • Handle: RePEc:bla:scjsta:v:48:y:2021:i:2:p:429-455
    DOI: 10.1111/sjos.12476
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12476
    Download Restriction: no

    File URL: https://libkey.io/10.1111/sjos.12476?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. Chung, Ching-Fan, 2002. "Sample Means, Sample Autocovariances, And Linear Regression Of Stationary Multivariate Long Memory Processes," Econometric Theory, Cambridge University Press, vol. 18(1), pages 51-78, February.
    2. Herrmann, Eva & Ziegler, Klaus, 2004. "Rates of consistency for nonparametric estimation of the mode in absence of smoothness assumptions," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 359-368, July.
    3. Grahovac, Danijel & Leonenko, Nikolai N. & Taqqu, Murad S., 2019. "Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5113-5150.
    4. Walther G., 2002. "Detecting the Presence of Mixing with Multiscale Maximum Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 508-513, June.
    5. M.‐Y. Cheng & P. Hall, 1998. "Calibrating the excess mass and dip tests of modality," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 579-589.
    6. K. S. Chan, 2004. "Testing for multimodality with dependent data," Biometrika, Biometrika Trust, vol. 91(1), pages 113-123, March.
    7. Joseph Romano, 1988. "Bootstrapping the mode," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(3), pages 565-586, September.
    8. Sucharita Ghosh & Jan Beran, 2006. "On Estimating the Cumulant Generating Function of Linear Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 53-71, March.
    9. P. M. Hartigan, 1985. "Computation of the Dip Statistic to Test for Unimodality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 320-325, November.
    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. Natalie Neumeyer & Miguel A. Delgado & Lajos Horváth & Simos Meintanis & Emanuele Taufer & Lixing Zhu, 2021. "4th Workshop on Goodness‐of‐Fit, Change‐Point, and Related Problems, Trento, 2019," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 371-374, June.

    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. James Mitchell & Aubrey Poon & Dan Zhu, 2022. "Constructing Density Forecasts from Quantile Regressions: Multimodality in Macro-Financial Dynamics," Working Papers 22-12R, Federal Reserve Bank of Cleveland, revised 11 Apr 2023.
    2. Suren Basov & Svetlana Danilkina & David Prentice, 2020. "When Does Variety Increase with Quality?," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 56(3), pages 463-487, May.
    3. Jose Ameijeiras-Alonso & Rosa M. Crujeiras & Alberto Rodríguez-Casal, 2019. "Mode testing, critical bandwidth and excess mass," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 900-919, September.
    4. Feng Zhu, 2005. "A nonparametric analysis of the shape dynamics of the US personal income distribution: 1962-2000," BIS Working Papers 184, Bank for International Settlements.
    5. Mikael Juselius & Nikola Tarashev, 2022. "When uncertainty decouples expected and unexpected losses," BIS Working Papers 995, Bank for International Settlements.
    6. Mikael Juselius & Nikola Tarashev, 2022. "When uncertainty decouples expected and unexpected losses," BIS Working Papers 995, Bank for International Settlements.
    7. repec:zbw:bofrdp:2022_004 is not listed on IDEAS
    8. van Dijk, Dick & Hans Franses, Philip & Peter Boswijk, H., 2007. "Absorption of shocks in nonlinear autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4206-4226, May.
    9. Daniel J. Henderson & Christopher F. Parmeter & R. Robert Russell, 2008. "Modes, weighted modes, and calibrated modes: evidence of clustering using modality tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 607-638.
    10. Di, J. & Kolaczyk, E., 2010. "Complexity-penalized estimation of minimum volume sets for dependent data," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1910-1926, October.
    11. Mariani, Fabio & Pérez-Barahona, Agustín & Raffin, Natacha, 2010. "Life expectancy and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 798-815, April.
    12. Deversi, Marvin & Ispano, Alessandro & Schwardmann, Peter, 2021. "Spin doctors: An experiment on vague disclosure," European Economic Review, Elsevier, vol. 139(C).
    13. Joerg Heining & Joerg Lingens, 2000. "Social Interaction in Regional Labour Markets," Regional and Urban Modeling 283600034, EcoMod.
    14. Graham Elliott & Nikolay Kudrin & Kaspar Wüthrich, 2022. "Detecting p‐Hacking," Econometrica, Econometric Society, vol. 90(2), pages 887-906, March.
    15. Pfister, Roland & Wirth, Robert & Weller, Lisa & Foerster, Anna & Schwarz, Katharina, 2018. "Taking shortcuts: Cognitive conflict during motivated rule-breaking," MPRA Paper 95773, University Library of Munich, Germany.
    16. John Ryter & Xinkai Fu & Karan Bhuwalka & Richard Roth & Elsa Olivetti, 2022. "Assessing recycling, displacement, and environmental impacts using an economics‐informed material system model," Journal of Industrial Ecology, Yale University, vol. 26(3), pages 1010-1024, June.
    17. Utz Weitzel & Michael Kirchler, 2022. "The Banker's Oath And Financial Advice," Working Papers 2022-13, Faculty of Economics and Statistics, Universität Innsbruck.
    18. Farzad Sabzikar & Qiying Wang & Peter C.B. Phillips, 2018. "Asymptotic Theory for Near Integrated Process Driven by Tempered Linear Process," Cowles Foundation Discussion Papers 2131, Cowles Foundation for Research in Economics, Yale University.
    19. Ouafae Benrabah & Elias Ould Saïd & Abdelkader Tatachak, 2015. "A kernel mode estimate under random left truncation and time series model: asymptotic normality," Statistical Papers, Springer, vol. 56(3), pages 887-910, August.
    20. Beth Fairfield & Ettore Ambrosini & Nicola Mammarella & Maria Montefinese, 2017. "Affective Norms for Italian Words in Older Adults: Age Differences in Ratings of Valence, Arousal and Dominance," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-22, January.
    21. Cavallo, Alberto & Rigobon, Roberto, 2011. "The Distribution of the Size of Price Changes," Working Papers 2011-011, Banco Central de Reserva del Perú.

    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:48:y:2021:i:2:p:429-455. 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.