IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v216y2025ics0167715224002232.html
   My bibliography  Save this article

Information bounds for Gaussian copula parameter in stationary semiparametric Markov models

Author

Listed:
  • Chen, Xiaohong
  • Yi, Yanping

Abstract

Let {Vt}t=1n be any univariate stationary first-order semiparametric Markov process generated from an unknown invariant marginal distribution and a bivariate Gaussian copula with unknown correlation coefficient α0∈(−1,1). We prove that 1−α02 is the semiparametric efficient variance bound for estimating the correlation parameter α0 in any Gaussian copula generated first-order stationary Markov models. Surprisingly, this variance bound is strictly larger than 1−α022 (when α0≠0), which is the semiparametric efficient variance bound derived by Klaassen and Wellner (1997) for estimating the correlation parameter using any i.i.d. data {(Xi,Yi)}i=1n generated from a bivariate Gaussian copula with two unknown marginal distributions.

Suggested Citation

  • Chen, Xiaohong & Yi, Yanping, 2025. "Information bounds for Gaussian copula parameter in stationary semiparametric Markov models," Statistics & Probability Letters, Elsevier, vol. 216(C).
  • Handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002232
    DOI: 10.1016/j.spl.2024.110254
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224002232
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2024.110254?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. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    2. Xiaohong Chen & Wei Biao Wu & Yanping Yi, 2009. "Efficient Estimation of Copula-based Semiparametric Markov Models," Cowles Foundation Discussion Papers 1691, Cowles Foundation for Research in Economics, Yale University, revised Mar 2009.
    3. Fan, Yanqin & Han, Fang & Park, Hyeonseok, 2023. "Estimation and inference in a high-dimensional semiparametric Gaussian copula vector autoregressive model," Journal of Econometrics, Elsevier, vol. 237(1).
    4. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1165-1185, December.
    5. Ibragimov, Rustam, 2009. "Copula-Based Characterizations For Higher Order Markov Processes," Econometric Theory, Cambridge University Press, vol. 25(3), pages 819-846, June.
    6. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    7. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    8. Segers, Johan & Van den Akker, Ramon & Werker, Bas, 2014. "Semiparametric Gaussian copula models: Geometry and efficient rank-based Estimation," LIDAM Reprints ISBA 2014021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Chen, Xiaohong & Xiao, Zhijie & Wang, Bo, 2022. "Copula-based time series with filtered nonstationarity," Journal of Econometrics, Elsevier, vol. 228(1), pages 127-155.
    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. Rubén Loaiza‐Maya & Michael S. Smith & Worapree Maneesoonthorn, 2018. "Time series copulas for heteroskedastic data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 332-354, April.
    2. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(5), pages 923-960, October.
    3. Liang Zhu & Christine Lim & Wenjun Xie & Yuan Wu, 2017. "Analysis of tourism demand serial dependence structure for forecasting," Tourism Economics, , vol. 23(7), pages 1419-1436, November.
    4. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    5. Chen, Xiaohong & Xiao, Zhijie & Wang, Bo, 2022. "Copula-based time series with filtered nonstationarity," Journal of Econometrics, Elsevier, vol. 228(1), pages 127-155.
    6. Bladt, Martin & McNeil, Alexander J., 2022. "Time series copula models using d-vines and v-transforms," Econometrics and Statistics, Elsevier, vol. 24(C), pages 27-48.
    7. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2013. "Estimating non-linear serial and cross-interdependence between financial assets," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 837-846.
    8. Alexander J. McNeil, 2020. "Modelling volatile time series with v-transforms and copulas," Papers 2002.10135, arXiv.org, revised Jan 2021.
    9. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105, arXiv.org.
    10. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    11. Nagler, Thomas & Krüger, Daniel & Min, Aleksey, 2022. "Stationary vine copula models for multivariate time series," Journal of Econometrics, Elsevier, vol. 227(2), pages 305-324.
    12. Martin Bladt & Alexander J. McNeil, 2020. "Time series copula models using d-vines and v-transforms," Papers 2006.11088, arXiv.org, revised Jul 2021.
    13. Overbeck Ludger & Schmidt Wolfgang M., 2015. "Multivariate Markov Families of Copulas," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-13, October.
    14. Brendan K. Beare & Juwon Seo, 2015. "Vine Copula Specifications for Stationary Multivariate Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 228-246, March.
    15. Oleg Sokolinskiy & Dick van Dijk, 2011. "Forecasting Volatility with Copula-Based Time Series Models," Tinbergen Institute Discussion Papers 11-125/4, Tinbergen Institute.
    16. Aristidis K. Nikoloulopoulos & Peter G. Moffatt, 2019. "Coupling Couples With Copulas: Analysis Of Assortative Matching On Risk Attitude," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 654-666, January.
    17. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1165-1185, December.
    18. Bu, Ruijun & Hadri, Kaddour & Kristensen, Dennis, 2021. "Diffusion copulas: Identification and estimation," Journal of Econometrics, Elsevier, vol. 221(2), pages 616-643.
    19. Cherubini, Umberto & Mulinacci, Sabrina & Romagnoli, Silvia, 2011. "A copula-based model of speculative price dynamics in discrete time," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1047-1063, July.
    20. Shi, Peng & Zhao, Zifeng, 2024. "Enhanced pricing and management of bundled insurance risks with dependence-aware prediction using pair copula construction," Journal of Econometrics, Elsevier, vol. 240(1).

    More about this item

    Keywords

    Gaussian copula; First-order Markov models; Semiparametric Fisher information bound;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    Statistics

    Access and download statistics

    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:216:y:2025:i:c:s0167715224002232. 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.