IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v105y2015icp47-56.html
   My bibliography  Save this article

Asymptotics for a class of dependent random variables

Author

Listed:
  • Zhang, Li-Xin
  • Zhang, Yang

Abstract

We consider a class of dependent random variables where the dependence structure involves a factor driven by Sn/n. Under very mild conditions for the innovation, we obtain several asymptotic results for the partial sums including basic asymptotics and strong limit theorems. The fact that the asymptotic properties differ strikingly in a neighbour of a critical point makes the model very interesting.

Suggested Citation

  • Zhang, Li-Xin & Zhang, Yang, 2015. "Asymptotics for a class of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 47-56.
    • Handle: RePEc:eee:stapro:v:105:y:2015:i:c:p:47-56
    DOI: 10.1016/j.spl.2015.05.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215001790
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.05.018?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. Peligrad, Magda & Sang, Hailin, 2012. "Asymptotic Properties Of Self-Normalized Linear Processes With Long Memory," Econometric Theory, Cambridge University Press, vol. 28(3), pages 548-569, June.
    2. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas & Koul, Hira L., 2014. "Asymptotic Normality For Weighted Sums Of Linear Processes," Econometric Theory, Cambridge University Press, vol. 30(1), pages 252-284, February.
    3. C.C. Heyde, 2004. "Asymptotics and Criticality for a Correlated Bernoulli Process," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 46(1), pages 53-57, March.
    4. James, Barry & James, Kang & Qi, Yongcheng, 2008. "Limit theorems for correlated Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2339-2345, October.
    5. Wu, Lan & Qi, Yongcheng & Yang, Jingping, 2012. "Asymptotics for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 455-463.
    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. Gava, Renato J. & Rezende, Bruna L.F., 2021. "Some limit theorems for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 170(C).
    2. Zhang, Yang & Zhang, Li-Xin, 2015. "On the almost sure invariance principle for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 264-271.
    3. Gut, Allan & Stadtmüller, Ulrich, 2022. "The elephant random walk with gradually increasing memory," Statistics & Probability Letters, Elsevier, vol. 189(C).
    4. Wu, Lan & Qi, Yongcheng & Yang, Jingping, 2012. "Asymptotics for dependent Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 455-463.
    5. Damgaard, Christian, 2008. "Modelling pin-point plant cover data along an environmental gradient," Ecological Modelling, Elsevier, vol. 214(2), pages 404-410.
    6. Liudas Giraitis & Donatas Surgailis & Andrius Škarnulis, 2015. "Integrated ARCH, FIGARCH and AR Models: Origins of Long Memory," Working Papers 766, Queen Mary University of London, School of Economics and Finance.
    7. Alessandro Arlotto & Noah Gans & J. Michael Steele, 2014. "Markov Decision Problems Where Means Bound Variances," Operations Research, INFORMS, vol. 62(4), pages 864-875, August.
    8. Jing Dong & Rouba Ibrahimb, 2020. "Managing Supply in the On-Demand Economy: Flexible Workers, Full-Time Employees, or Both?," Operations Research, INFORMS, vol. 68(4), pages 1238-1264, July.
    9. Paul Doukhan & Ieva Grublytė & Denys Pommeret & Laurence Reboul, 2020. "Comparing the marginal densities of two strictly stationary linear processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1419-1447, December.
    10. Timothy Fortune & Magda Peligrad & Hailin Sang, 2021. "A local limit theorem for linear random fields," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 696-710, September.
    11. Modarres, Reza, 2011. "High-dimensional generation of Bernoulli random vectors," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1136-1142, August.
    12. Liudas Giraitis & George Kapetanios & Tony Yates, 2018. "Inference on Multivariate Heteroscedastic Time Varying Random Coefficient Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(2), pages 129-149, March.
    13. Liudas Giraitis & Donatas Surgailis & Andrius Škarnulis, 2015. "Integrated ARCH, FIGARCH and AR Models: Origins of Long Memory," Working Papers 766, Queen Mary University of London, School of Economics and Finance.
    14. Masoud M. Nasari & Mohamedou Ould-Haye, 2022. "Confidence intervals with higher accuracy for short and long-memory linear processes," Statistical Papers, Springer, vol. 63(4), pages 1187-1220, August.
    15. Hassler, Uwe & Hosseinkouchack, Mehdi, 2020. "Estimating the mean under strong persistence," Economics Letters, Elsevier, vol. 188(C).
    16. Magda Peligrad & Hailin Sang, 2013. "Central Limit Theorem for Linear Processes with Infinite Variance," Journal of Theoretical Probability, Springer, vol. 26(1), pages 222-239, March.
    17. James, Barry & James, Kang & Qi, Yongcheng, 2008. "Limit theorems for correlated Bernoulli random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2339-2345, October.
    18. Peligrad, Magda & Sang, Hailin & Xiao, Yimin & Yang, Guangyu, 2022. "Limit theorems for linear random fields with innovations in the domain of attraction of a stable law," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 596-621.
    19. Zhang, Rong-Mao & Sin, Chor-yiu (CY) & Ling, Shiqing, 2015. "On functional limits of short- and long-memory linear processes with GARCH(1,1) noises," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 482-512.
    20. Peter Farkas & Laszlo Matyas, 2015. "Testing for Unit Roots in Panel Data with Boundary Crossing Counts," CEU Working Papers 2015_5, Department of Economics, Central European University, revised 03 Nov 2015.

    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:105:y:2015:i:c:p:47-56. 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.