IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v151y2019icp1-7.html
   My bibliography  Save this article

Covariance functions on spheres cross time: Beyond spatial isotropy and temporal stationarity

Author

Listed:
  • Estrade, Anne
  • Fariñas, Alessandra
  • Porcu, Emilio

Abstract

Spectral representations uniquely define the covariance functions associated to random fields defined over spheres or spheres cross time. Covariance functions on spheres cross time are usually modeled under the assumptions of either spatial isotropy or axial symmetry, and the assumption of temporal stationarity. This paper goes beyond these assumptions. In particular, we consider the problem of spatially anisotropic covariance functions on spheres. The crux of our criterion is to escape from the addition theorem for spherical harmonics. We also challenge the problem of temporal nonstationarity in nonseparable space–time covariance functions, where space is the n-dimensional sphere.

Suggested Citation

  • Estrade, Anne & Fariñas, Alessandra & Porcu, Emilio, 2019. "Covariance functions on spheres cross time: Beyond spatial isotropy and temporal stationarity," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 1-7.
    • Handle: RePEc:eee:stapro:v:151:y:2019:i:c:p:1-7
    DOI: 10.1016/j.spl.2019.03.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715219300872
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.03.011?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. Emilio Porcu & Alfredo Alegria & Reinhard Furrer, 2018. "Modeling Temporally Evolving and Spatially Globally Dependent Data," International Statistical Review, International Statistical Institute, vol. 86(2), pages 344-377, August.
    2. Emilio Porcu & Moreno Bevilacqua & Marc G. Genton, 2016. "Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 888-898, April.
    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. Emilio Porcu & Philip A. White, 2022. "Random fields on the hypertorus: Covariance modeling and applications," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.

    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. Alessia Caponera, 2021. "SPHARMA approximations for stationary functional time series on the sphere," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 609-634, October.
    2. Cleanthous, Galatia & Georgiadis, Athanasios G. & Lang, Annika & Porcu, Emilio, 2020. "Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4873-4891.
    3. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    4. Bingham, N.H. & Symons, Tasmin L., 2019. "Dimension walks on Sd×R," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 12-17.
    5. Li, Yang & Zhu, Zhengyuan, 2016. "Modeling nonstationary covariance function with convolution on sphere," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 233-246.
    6. Luciano Telesca & Fabian Guignard & Nora Helbig & Mikhail Kanevski, 2019. "Wavelet Scale Variance Analysis of Wind Extremes in Mountainous Terrains," Energies, MDPI, vol. 12(16), pages 1-10, August.
    7. Moreno Bevilacqua & Christian Caamaño‐Carrillo & Reinaldo B. Arellano‐Valle & Víctor Morales‐Oñate, 2021. "Non‐Gaussian geostatistical modeling using (skew) t processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 212-245, March.
    8. Emilio Porcu & Philip A. White, 2022. "Random fields on the hypertorus: Covariance modeling and applications," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.
    9. Tingjin Chu & Jialuo Liu & Jun Zhu & Haonan Wang, 2022. "Spatio-Temporal Expanding Distance Asymptotic Framework for Locally Stationary Processes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 689-713, August.
    10. Emery, Xavier & Furrer, Reinhard & Porcu, Emilio, 2019. "A turning bands method for simulating isotropic Gaussian random fields on the sphere," Statistics & Probability Letters, Elsevier, vol. 144(C), pages 9-15.
    11. Laura M. Sangalli, 2021. "Spatial Regression With Partial Differential Equation Regularisation," International Statistical Review, International Statistical Institute, vol. 89(3), pages 505-531, December.
    12. Fassò, A. & Finazzi, F. & Madonna, F., 2018. "Statistical issues in radiosonde observation of atmospheric temperature and humidity profiles," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 97-100.
    13. Guella, Jean Carlo & Menegatto, Valdir Antonio & Porcu, Emilio, 2018. "Strictly positive definite multivariate covariance functions on spheres," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 150-159.
    14. Montero, José-María, 2018. "Geostatistics: Unde venis et quo vadis? /Geoestadística:¿De dónde vienes y a dónde vas?," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 36, pages 81-106, Enero.
    15. Moreno Bevilacqua & Christian Caamaño-Carrillo & Reinaldo B. Arellano-Valle & Camilo Gómez, 2022. "A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 644-674, September.
    16. Muhammad Umar Javed & Nadeem Javaid & Abdulaziz Aldegheishem & Nabil Alrajeh & Muhammad Tahir & Muhammad Ramzan, 2020. "Scheduling Charging of Electric Vehicles in a Secured Manner by Emphasizing Cost Minimization Using Blockchain Technology and IPFS," Sustainability, MDPI, vol. 12(12), pages 1-37, June.
    17. Liu, Jialuo & Chu, Tingjin & Zhu, Jun & Wang, Haonan, 2021. "Semiparametric method and theory for continuously indexed spatio-temporal processes," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    18. Bissiri, Pier Giovanni & Cleanthous, Galatia & Emery, Xavier & Nipoti, Bernardo & Porcu, Emilio, 2022. "Nonparametric Bayesian modelling of longitudinally integrated covariance functions on spheres," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    19. Caponera, Alessia & Durastanti, Claudio & Vidotto, Anna, 2021. "LASSO estimation for spherical autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 167-199.
    20. Anna Gloria Billé & Leopoldo Catania, 2018. "Dynamic Spatial Autoregressive Models with Time-varying Spatial Weighting Matrices," BEMPS - Bozen Economics & Management Paper Series BEMPS55, Faculty of Economics and Management at the Free University of Bozen.

    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:stapro:v:151:y:2019:i:c:p:1-7. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/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.