IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v33y2024i2d10.1007_s11749-023-00913-7.html
   My bibliography  Save this article

LRD spectral analysis of multifractional functional time series on manifolds

Author

Listed:
  • Diana P. Ovalle–Muñoz

    (University of Granada)

  • M. Dolores Ruiz–Medina

    (University of Granada)

Abstract

This paper addresses the estimation of the second-order structure of a manifold cross-time random field (RF) displaying spatially varying Long Range Dependence (LRD), adopting the functional time series framework introduced in Ruiz-Medina (Fract Calc Appl Anal 25:1426–1458, 2022). Conditions for the asymptotic unbiasedness of the integrated periodogram operator in the Hilbert–Schmidt operator norm are derived beyond structural assumptions. Weak-consistent estimation of the long-memory operator is achieved under a semiparametric functional spectral framework in the Gaussian context. The case where the projected manifold process can display Short Range Dependence (SRD) and LRD at different manifold scales is also analyzed. The performance of both estimation procedures is illustrated in the simulation study, in the context of multifractionally integrated spherical functional autoregressive–moving average (SPHARMA(p,q)) processes.

Suggested Citation

  • Diana P. Ovalle–Muñoz & M. Dolores Ruiz–Medina, 2024. "LRD spectral analysis of multifractional functional time series on manifolds," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(2), pages 564-588, June.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:2:d:10.1007_s11749-023-00913-7
    DOI: 10.1007/s11749-023-00913-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-023-00913-7
    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/s11749-023-00913-7?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. Tomáš Rubín & Victor M. Panaretos, 2020. "Functional lagged regression with sparse noisy observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 858-882, November.
    2. Galatia Cleanthous & Emilio Porcu & Philip White, 2021. "Regularity and approximation of Gaussian random fields evolving temporally over compact two-point homogeneous spaces," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 836-860, December.
    3. Shahin Tavakoli & Victor M. Panaretos, 2016. "Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1020-1035, July.
    4. D’Ovidio, Mirko & Leonenko, Nikolai & Orsingher, Enzo, 2016. "Fractional spherical random fields," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 146-156.
    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. Tomáš Rubín & Victor M. Panaretos, 2020. "Functional lagged regression with sparse noisy observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 858-882, November.
    2. Gregory Rice & Han Lin Shang, 2017. "A Plug-in Bandwidth Selection Procedure for Long-Run Covariance Estimation with Stationary Functional Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(4), pages 591-609, July.
    3. 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.
    4. Marek Vochozka & Andrea Bláhová & Zuzana Rowland, 2022. "Is Platinum a Real Store of Wealth?," IJFS, MDPI, vol. 10(3), pages 1-23, August.
    5. Valentina Masarotto & Victor M. Panaretos & Yoav Zemel, 2019. "Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 172-213, February.
    6. Leonenko, N.N. & Papić, I. & Sikorskii, A. & Šuvak, N., 2017. "Heavy-tailed fractional Pearson diffusions," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3512-3535.
    7. Valentina Masarotto & Guido Masarotto, 2024. "Covariance‐based soft clustering of functional data based on the Wasserstein–Procrustes metric," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(2), pages 485-512, June.
    8. Leucht, Anne & Paparoditis, Efstathios & Rademacher, Daniel & Sapatinas, Theofanis, 2022. "Testing equality of spectral density operators for functional processes," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

    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:testjl:v:33:y:2024:i:2:d:10.1007_s11749-023-00913-7. 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.