IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v129y2019i7p2466-2484.html
   My bibliography  Save this article

ℓ1-symmetric vector random fields

Author

Listed:
  • Wang, Fangfang
  • Ma, Chunsheng

Abstract

This paper studies the properties of ℓ1-symmetric vector random fields in Rd, whose direct/cross covariances are functions of ℓ1-norm. The spectral representation and a turning bands expression of the covariance matrix function are derived for an ℓ1-symmetric vector random field that is mean square continuous. We also establish an integral relationship between an ℓ1-symmetric covariance matrix function and an isotropic one. In addition, a simple but efficient approach is proposed to construct the ℓ1-symmetric random field in Rd, whose univariate marginal distributions may be taken as arbitrary infinitely divisible distribution with finite variance.

Suggested Citation

  • Wang, Fangfang & Ma, Chunsheng, 2019. "ℓ1-symmetric vector random fields," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2466-2484.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:7:p:2466-2484
    DOI: 10.1016/j.spa.2018.07.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918303302
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2018.07.012?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. Brockwell, Peter J. & Lindner, Alexander, 2009. "Existence and uniqueness of stationary Lévy-driven CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2660-2681, August.
    2. Brockwell, Peter J. & Schlemm, Eckhard, 2013. "Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 217-251.
    3. Richard Finlay & Thomas Fung & Eugene Seneta, 2011. "Autocorrelation Functions," International Statistical Review, International Statistical Institute, vol. 79(2), pages 255-271, August.
    4. Rustam Ibragimov & Artem Prokhorov, 2017. "Heavy Tails and Copulas:Topics in Dependence Modelling in Economics and Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9644, September.
    5. Renxiang Wang & Juan Du & Chunsheng Ma, 2014. "Covariance Matrix Functions of Isotropic Vector Random Fields," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2081-2093, May.
    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. Linzenich, Anika & Arning, Katrin & Bongartz, Dominik & Mitsos, Alexander & Ziefle, Martina, 2019. "What fuels the adoption of alternative fuels? Examining preferences of German car drivers for fuel innovations," Applied Energy, Elsevier, vol. 249(C), pages 222-236.

    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. Vicky Fasen & Florian Fuchs, 2013. "Spectral estimates for high-frequency sampled continuous-time autoregressive moving average processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 532-551, September.
    2. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    3. Dietmar Pfeifer & Olena Ragulina, 2018. "Generating VaR Scenarios under Solvency II with Product Beta Distributions," Risks, MDPI, vol. 6(4), pages 1-15, October.
    4. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas, 2022. "The Heavy-Tailed Gleser Model: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    5. Fahim Afzal & Pan Haiying & Farman Afzal & Asif Mahmood & Amir Ikram, 2021. "Value-at-Risk Analysis for Measuring Stochastic Volatility of Stock Returns: Using GARCH-Based Dynamic Conditional Correlation Model," SAGE Open, , vol. 11(1), pages 21582440211, March.
    6. Jorge Ignacio Gonz'alez C'azares & Aleksandar Mijatovi'c & Ger'onimo Uribe Bravo, 2018. "Geometrically Convergent Simulation of the Extrema of L\'{e}vy Processes," Papers 1810.11039, arXiv.org, revised Jun 2021.
    7. Peter J. Brockwell & Yasumasa Matsuda, 2015. "Levy-driven CARMA Random Fields on Rn," TERG Discussion Papers 339, Graduate School of Economics and Management, Tohoku University.
    8. Péter Kevei, 2018. "Asymptotic moving average representation of high-frequency sampled multivariate CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 467-487, April.
    9. Pham, Viet Son, 2020. "Lévy-driven causal CARMA random fields," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7547-7574.
    10. Das, Bikramjit & Fasen-Hartmann, Vicky, 2024. "On heavy-tailed risks under Gaussian copula: The effects of marginal transformation," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    11. Mayerhofer, Eberhard & Stelzer, Robert & Vestweber, Johanna, 2020. "Geometric ergodicity of affine processes on cones," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4141-4173.
    12. Robin Merkle & Andrea Barth, 2023. "On Properties and Applications of Gaussian Subordinated Lévy Fields," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-33, June.
    13. Spangenberg, Felix, 2013. "Strictly stationary solutions of ARMA equations in Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 127-138.
    14. Tianshi Lu & Chunsheng Ma, 2020. "Isotropic Covariance Matrix Functions on Compact Two-Point Homogeneous Spaces," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1630-1656, September.
    15. Chanelle Duley & Prasanna Gai, 2023. "Macroeconomic tail risk, currency crises and the inter‐war gold standard," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 56(4), pages 1551-1582, November.
    16. Damette, Olivier & Goutte, Stéphane, 2023. "Beyond climate and conflict relationships: New evidence from a Copula-based analysis on an historical perspective," Journal of Comparative Economics, Elsevier, vol. 51(1), pages 295-323.
    17. Basse-O’Connor, Andreas & Nielsen, Mikkel Slot & Pedersen, Jan & Rohde, Victor, 2019. "Multivariate stochastic delay differential equations and CAR representations of CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4119-4143.
    18. Brockwell, Peter J. & Lindner, Alexander, 2015. "CARMA processes as solutions of integral equations," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 221-227.
    19. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
    20. Fred Espen Benth & Marco Piccirilli & Tiziano Vargiolu, 2017. "Additive energy forward curves in a Heath-Jarrow-Morton framework," Papers 1709.03310, arXiv.org, revised Jun 2018.

    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:129:y:2019:i:7:p:2466-2484. 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.