IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v122y2012i3p725-757.html
   My bibliography  Save this article

Functional convergence of stochastic integrals with application to statistical inference

Author

Listed:
  • Davis, Richard A.
  • Song, Li

Abstract

Assuming that {(Un,Vn)} is a sequence of càdlàg processes converging in distribution to (U,V) in the Skorohod topology, conditions are given under which {∬fn(β,u,v)dUndVn} converges weakly to ∬f(β,x,y)dUdV in the space C(R), where fn(β,u,v) is a sequence of “smooth” functions converging to f(β,u,v). Integrals of this form arise as the objective function for inference about a parameter β in a stochastic model. Convergence of these integrals play a key role in describing the asymptotics of the estimator of β which optimizes the objective function. We illustrate this with a moving average process.

Suggested Citation

  • Davis, Richard A. & Song, Li, 2012. "Functional convergence of stochastic integrals with application to statistical inference," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 725-757.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:725-757
    DOI: 10.1016/j.spa.2011.10.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911002687
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2011.10.007?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. Davis, Richard A. & Dunsmuir, William T.M., 1996. "Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 12(1), pages 1-29, March.
    2. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    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. Andreas S{o}jmark & Fabrice Wunderlich, 2023. "Functional CLTs for subordinated L\'evy models in physics, finance, and econometrics," Papers 2312.15119, arXiv.org, revised Jan 2024.

    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. Richard A. Davis & William T. M. Dunsmuir, 1997. "Least Absolute Deviation Estimation for Regression with ARMA Errors," Journal of Theoretical Probability, Springer, vol. 10(2), pages 481-497, April.
    2. Davis, Richard A. & Mikosch, Thomas, 1998. "Gaussian likelihood-based inference for non-invertible MA(1) processes with SS noise," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 99-122, September.
    3. Xinghui Wang & Wenjing Geng & Ruidong Han & Qifa Xu, 2023. "Asymptotic Properties of the M-estimation for an AR(1) Process with a General Autoregressive Coefficient," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-23, March.
    4. Yabe, Ryota, 2017. "Asymptotic distribution of the conditional-sum-of-squares estimator under moderate deviation from a unit root in MA(1)," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 220-226.
    5. Mohamed El Ghourabi & Christian Francq & Fedya Telmoudi, 2016. "Consistent Estimation of the Value at Risk When the Error Distribution of the Volatility Model is Misspecified," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 46-76, January.
    6. Zhu, Ke & Ling, Shiqing, 2013. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models," MPRA Paper 51509, University Library of Munich, Germany.
    7. Tilak Abeysinghe & Gulasekaran Rajaguru, 2009. "A Gaussian Test for Cointegration," Microeconomics Working Papers 22013, East Asian Bureau of Economic Research.
    8. D. M. Mahinda Samarakoon & Keith Knight, 2009. "A Note on Unit Root Tests with Infinite Variance Noise," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 314-334.
    9. Newbold, Paul & Leybourne, Stephen & Wohar, Mark E., 2001. "Trend-stationarity, difference-stationarity, or neither: further diagnostic tests with an application to U.S. Real GNP, 1875-1993," Journal of Economics and Business, Elsevier, vol. 53(1), pages 85-102.
    10. Andrews, Beth & Davis, Richard A. & Jay Breidt, F., 2006. "Maximum likelihood estimation for all-pass time series models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1638-1659, August.
    11. Chan, Ngai Hang & Zhang, Rong-Mao, 2009. "Quantile inference for near-integrated autoregressive time series under infinite variance and strong dependence," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4124-4148, December.
    12. Lynda Khalaf & Beatriz Peraza López, 2020. "Simultaneous Indirect Inference, Impulse Responses and ARMA Models," Econometrics, MDPI, vol. 8(2), pages 1-26, April.
    13. Meintanis, S. G. & Donatos, G. S., 1999. "Finite-sample performance of alternative estimators for autoregressive models in the presence of outliers," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 323-339, September.
    14. Francq, Christian & Zakoïan, Jean-Michel, 2015. "Risk-parameter estimation in volatility models," Journal of Econometrics, Elsevier, vol. 184(1), pages 158-173.
    15. Wu, Rongning, 2014. "Least absolute deviation estimation for general fractionally integrated autoregressive moving average time series models," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 69-76.
    16. Yuya Sasaki & Yulong Wang, 2020. "Testing Finite Moment Conditions for the Consistency and the Root-N Asymptotic Normality of the GMM and M Estimators," Papers 2006.02541, arXiv.org, revised Sep 2020.
    17. Chaohua Dong & Jiti Gao & Yundong Tu & Bin Peng, 2023. "Robust M-Estimation for Additive Single-Index Cointegrating Time Series Models," Papers 2301.06631, arXiv.org.
    18. Francq, Christian & Zakoïan, Jean-Michel, 2020. "Virtual Historical Simulation for estimating the conditional VaR of large portfolios," Journal of Econometrics, Elsevier, vol. 217(2), pages 356-380.
    19. Josef Arlt, 2023. "The problem of annual inflation rate indicator," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(3), pages 2772-2788, July.
    20. Fasen, Vicky, 2013. "Statistical estimation of multivariate Ornstein–Uhlenbeck processes and applications to co-integration," Journal of Econometrics, Elsevier, vol. 172(2), pages 325-337.

    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:122:y:2012:i:3:p:725-757. 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.