IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v183y2021ics0047259x21000063.html
   My bibliography  Save this article

Compound vectors of subordinators and their associated positive Lévy copulas

Author

Listed:
  • Riva-Palacio, Alan
  • Leisen, Fabrizio

Abstract

Lévy copulas are an important tool which can be used to build dependent Lévy processes. In a classical setting, they have been used to model financial applications. In a Bayesian framework they have been employed to introduce dependent nonparametric priors which allow to model heterogeneous data. This paper focuses on introducing a new class of Lévy copulas based on a class of subordinators recently appeared in the literature, called compound random measures. The well-known Clayton Lévy copula is a special case of this new class. Furthermore, we provide some novel results about the underlying vector of subordinators such as a series representation and relevant moments. The article concludes with an application to a Danish fire dataset.

Suggested Citation

  • Riva-Palacio, Alan & Leisen, Fabrizio, 2021. "Compound vectors of subordinators and their associated positive Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:jmvana:v:183:y:2021:i:c:s0047259x21000063
    DOI: 10.1016/j.jmva.2021.104728
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X21000063
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2021.104728?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. Grothe, Oliver & Nicklas, Stephan, 2013. "Vine constructions of Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 1-15.
    2. Kallsen, Jan & Tankov, Peter, 2006. "Characterization of dependence of multidimensional Lévy processes using Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1551-1572, August.
    3. Esmaeili, Habib & Klüppelberg, Claudia, 2010. "Parameter estimation of a bivariate compound Poisson process," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 224-233, October.
    4. Grothe, Oliver & Hofert, Marius, 2015. "Construction and sampling of Archimedean and nested Archimedean Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 182-198.
    5. Yuen, Kam C. & Guo, Junyi & Wu, Xueyuan, 2006. "On the first time of ruin in the bivariate compound Poisson model," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 298-308, April.
    6. Jim E. Griffin & Fabrizio Leisen, 2017. "Compound random measures and their use in Bayesian non-parametrics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 525-545, March.
    7. Habib Esmaeili & Claudia Klüppelberg, 2013. "Two-Step Estimation Of A Multi-Variate Lévy Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 668-690, November.
    8. Fuchang Gao & Lixing Han, 2012. "Implementing the Nelder-Mead simplex algorithm with adaptive parameters," Computational Optimization and Applications, Springer, vol. 51(1), pages 259-277, January.
    9. Riva Palacio, Alan & Leisen, Fabrizio, 2018. "Integrability conditions for compound random measures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 32-37.
    10. Esmaeili, Habib & Klüppelberg, Claudia, 2011. "Parametric estimation of a bivariate stable Lévy process," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 918-930, May.
    11. Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 482-495, March.
    12. Delignette-Muller, Marie Laure & Dutang, Christophe, 2015. "fitdistrplus: An R Package for Fitting Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i04).
    13. Patrizia Semeraro, 2008. "A Multivariate Variance Gamma Model For Financial Applications," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-18.
    14. Marie Laure Delignette-Muller & Christophe Dutang, 2015. "fitdistrplus : An R Package for Fitting Distributions," Post-Print hal-01616147, HAL.
    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. Vladimir Panov, 2017. "Series Representations for Multivariate Time-Changed Lévy Models," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 97-119, March.
    2. Beghin, Luisa & Macci, Claudio & Ricciuti, Costantino, 2020. "Random time-change with inverses of multivariate subordinators: Governing equations and fractional dynamics," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6364-6387.
    3. Grothe, Oliver & Nicklas, Stephan, 2013. "Vine constructions of Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 1-15.
    4. Habib Esmaeili & Claudia Klüppelberg, 2013. "Two-Step Estimation Of A Multi-Variate Lévy Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 668-690, November.
    5. Schulte, Benedikt & Sachs, Anna-Lena, 2020. "The price-setting newsvendor with Poisson demand," European Journal of Operational Research, Elsevier, vol. 283(1), pages 125-137.
    6. Avanzi, Benjamin & Taylor, Greg & Wang, Melantha & Wong, Bernard, 2021. "SynthETIC: An individual insurance claim simulator with feature control," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 296-308.
    7. K. G. Reddy & M. G. M. Khan, 2020. "stratifyR: An R Package for optimal stratification and sample allocation for univariate populations," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(3), pages 383-405, September.
    8. Chen, Shang & He, Liang & Cao, Yinxuan & Wang, Runhong & Wu, Lianhai & Wang, Zhao & Zou, Yufeng & Siddique, Kadambot H.M. & Xiong, Wei & Liu, Manshuang & Feng, Hao & Yu, Qiang & Wang, Xiaoming & He, J, 2021. "Comparisons among four different upscaling strategies for cultivar genetic parameters in rainfed spring wheat phenology simulations with the DSSAT-CERES-Wheat model," Agricultural Water Management, Elsevier, vol. 258(C).
    9. Oliver Grothe & Stephan Nicklas, 2012. "Vine Constructions of Levy Copulas," Papers 1207.4309, arXiv.org, revised Sep 2012.
    10. Riva Palacio, Alan & Leisen, Fabrizio, 2018. "Integrability conditions for compound random measures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 32-37.
    11. Minji Lee & Sun Ju Chung & Youngjo Lee & Sera Park & Jun-Gun Kwon & Dai Jin Kim & Donghwan Lee & Jung-Seok Choi, 2020. "Investigation of Correlated Internet and Smartphone Addiction in Adolescents: Copula Regression Analysis," IJERPH, MDPI, vol. 17(16), pages 1-12, August.
    12. Veronesi, F. & Grassi, S. & Raubal, M., 2016. "Statistical learning approach for wind resource assessment," Renewable and Sustainable Energy Reviews, Elsevier, vol. 56(C), pages 836-850.
    13. Phillip M. Gurman & Tom Ross & Andreas Kiermeier, 2018. "Quantitative Microbial Risk Assessment of Salmonellosis from the Consumption of Australian Pork: Minced Meat from Retail to Burgers Prepared and Consumed at Home," Risk Analysis, John Wiley & Sons, vol. 38(12), pages 2625-2645, December.
    14. Adam R. Martin & Rachel O. Mariani & Kimberley A. Cathline & Michael Duncan & Nicholas J. Paroshy & Gavin Robertson, 2022. "Soil Compaction Drives an Intra-Genotype Leaf Economics Spectrum in Wine Grapes," Agriculture, MDPI, vol. 12(10), pages 1-16, October.
    15. Héctor Nájera & David Gordon, 2023. "A Monte Carlo Study of Some Empirical Methods to Find the Optimal Poverty Line in Multidimensional Poverty Measurement," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 167(1), pages 391-419, June.
    16. Athanasios Zisos & Georgia-Konstantina Sakki & Andreas Efstratiadis, 2023. "Mixing Renewable Energy with Pumped Hydropower Storage: Design Optimization under Uncertainty and Other Challenges," Sustainability, MDPI, vol. 15(18), pages 1-21, September.
    17. Valentas Gruzauskas & Aurelija Burinskiene & Andrius Krisciunas, 2023. "Application of Information-Sharing for Resilient and Sustainable Food Delivery in Last-Mile Logistics," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    18. Amanda M. Wilson & Kelly A. Reynolds & Marc P. Verhougstraete & Robert A. Canales, 2019. "Validation of a Stochastic Discrete Event Model Predicting Virus Concentration on Nurse Hands," Risk Analysis, John Wiley & Sons, vol. 39(8), pages 1812-1824, August.
    19. Wang, Xialin & Nuppenau, Ernst-August, 2021. "Modelling payments for ecosystem services for solving future water conflicts at spatial scales: The Okavango River Basin example," Ecological Economics, Elsevier, vol. 184(C).
    20. Sarra Ghaddab & Manel Kacem & Christian Peretti & Lotfi Belkacem, 2023. "Extreme severity modeling using a GLM-GPD combination: application to an excess of loss reinsurance treaty," Empirical Economics, Springer, vol. 65(3), pages 1105-1127, September.

    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:jmvana:v:183:y:2021:i:c:s0047259x21000063. 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.