IDEAS home Printed from https://ideas.repec.org/a/spr/sistpr/v24y2021i3d10.1007_s11203-021-09244-6.html
   My bibliography  Save this article

SPHARMA approximations for stationary functional time series on the sphere

Author

Listed:
  • Alessia Caponera

    (Università di Roma Tor Vergata
    Ecole Polytechnique Fédérale de Lausanne)

Abstract

In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressions (SPHAR) recently studied in Caponera and Marinucci (Ann Stat 49(1):346–369, 2021) and Caponera et al. (Stoch Process Appl 137:167–199, 2021); more importantly, we then show that SPHAR and SPHARMA processes of sufficiently large order can be exploited to approximate every isotropic and stationary sphere-cross-time random field, thus generalizing to this infinite-dimensional framework some classical results on real-valued stationary processes. Further characterizations in terms of functional spectral representation theorems and Wold-like decompositions are also established.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:3:d:10.1007_s11203-021-09244-6
    DOI: 10.1007/s11203-021-09244-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11203-021-09244-6
    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/s11203-021-09244-6?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. Jun, Mikyoung, 2014. "Matérn-based nonstationary cross-covariance models for global processes," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 134-146.
    2. 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.
    3. Panaretos, Victor M. & Tavakoli, Shahin, 2013. "Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2779-2807.
    4. 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.
    5. Mas, André, 2002. "Weak convergence for the covariance operators of a Hilbertian linear process," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 117-135, May.
    6. Denis Bosq, 2002. "Estimation of Mean and Covariance Operator of Autoregressive Processes in Banach Spaces," Statistical Inference for Stochastic Processes, Springer, vol. 5(3), pages 287-306, October.
    7. van Delft, Anne & Eichler, Michael, 2020. "A note on Herglotz’s theorem for time series on function spaces," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3687-3710.
    8. Gneiting T., 2002. "Nonseparable, Stationary Covariance Functions for Space-Time Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 590-600, June.
    9. 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.
    10. Herold Dehling & Olimjon Sharipov, 2005. "Estimation of Mean and Covariance Operator for Banach Space Valued Autoregressive Processes with Dependent Innovations," Statistical Inference for Stochastic Processes, Springer, vol. 8(2), pages 137-149, September.
    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. van Delft, Anne, 2020. "A note on quadratic forms of stationary functional time series under mild conditions," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4206-4251.
    2. Álvarez-Liébana, Javier & Bosq, Denis & Ruiz-Medina, María D., 2016. "Consistency of the plug-in functional predictor of the Ornstein–Uhlenbeck process in Hilbert and Banach spaces," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 12-22.
    3. Horta, Eduardo & Ziegelmann, Flavio, 2018. "Conjugate processes: Theory and application to risk forecasting," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 727-755.
    4. Axel Bücher & Holger Dette & Florian Heinrichs, 2020. "Detecting deviations from second-order stationarity in locally stationary functional time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 1055-1094, August.
    5. 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.
    6. Panaretos, Victor M. & Tavakoli, Shahin, 2013. "Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2779-2807.
    7. Ruiz-Medina, María D. & Álvarez-Liébana, Javier, 2019. "Strongly consistent autoregressive predictors in abstract Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 186-201.
    8. 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.
    9. 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.
    10. 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.
    11. van Delft, Anne & Eichler, Michael, 2017. "Locally Stationary Functional Time Series," LIDAM Discussion Papers ISBA 2017023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Laura M. Sangalli, 2021. "Spatial Regression With Partial Differential Equation Regularisation," International Statistical Review, International Statistical Institute, vol. 89(3), pages 505-531, December.
    13. 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.
    14. Zhang, Xianyang, 2016. "White noise testing and model diagnostic checking for functional time series," Journal of Econometrics, Elsevier, vol. 194(1), pages 76-95.
    15. Amira Elayouty & Marian Scott & Claire Miller, 2022. "Time-Varying Functional Principal Components for Non-Stationary EpCO $$_2$$ 2 in Freshwater Systems," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 506-522, September.
    16. 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.
    17. Yasumasa Matsuda, 2014. "Wavelet Analysis Of Spatio-Temporal Data," TERG Discussion Papers 311, Graduate School of Economics and Management, Tohoku University.
    18. 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.
    19. 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.
    20. Kokoszka, Piotr & Reimherr, Matthew & Wölfing, Nikolas, 2016. "A randomness test for functional panels," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 37-53.

    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:sistpr:v:24:y:2021:i:3:d:10.1007_s11203-021-09244-6. 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.