IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v127y2017i8p2751-2779.html
   My bibliography  Save this article

Scaling transition for nonlinear random fields with long-range dependence

Author

Listed:
  • Pilipauskaitė, Vytautė
  • Surgailis, Donatas

Abstract

We obtain a complete description of anisotropic scaling limits and the existence of scaling transition for nonlinear functions (Appell polynomials) of stationary linear random fields on Z2 with moving average coefficients decaying at possibly different rate in the horizontal and the vertical direction. The paper extends recent results on scaling transition for linear random fields in Puplinskaitė and Surgailis (2015, 2016).

Suggested Citation

  • Pilipauskaitė, Vytautė & Surgailis, Donatas, 2017. "Scaling transition for nonlinear random fields with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2751-2779.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:8:p:2751-2779
    DOI: 10.1016/j.spa.2016.12.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414917300030
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2016.12.011?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. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    2. Breuer, Péter & Major, Péter, 1983. "Central limit theorems for non-linear functionals of Gaussian fields," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 425-441, September.
    3. Hira Koul & Nao Mimoto & Donatas Surgailis, 2016. "A goodness-of-fit test for marginal distribution of linear random fields with long memory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 165-193, February.
    4. Biermé, Hermine & Meerschaert, Mark M. & Scheffler, Hans-Peter, 2007. "Operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 312-332, March.
    5. Puplinskaitė, Donata & Surgailis, Donatas, 2015. "Scaling transition for long-range dependent Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2256-2271.
    6. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2015. "Joint aggregation of random-coefficient AR(1) processes with common innovations," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 73-82.
    7. Lahiri, S.N. & Robinson, Peter M., 2016. "Central limit theorems for long range dependent spatial linear processes," LSE Research Online Documents on Economics 65331, London School of Economics and Political Science, LSE Library.
    8. Frédéric Lavancier, 2007. "Invariance principles for non-isotropic long memory random fields," Statistical Inference for Stochastic Processes, Springer, vol. 10(3), pages 255-282, October.
    9. Guo, Hongwen & Lim, Chae Young & Meerschaert, Mark M., 2009. "Local Whittle estimator for anisotropic random fields," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 993-1028, May.
    10. Bai, Shuyang & Taqqu, Murad S., 2014. "Generalized Hermite processes, discrete chaos and limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1710-1739.
    11. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2014. "Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1011-1035.
    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. Surgailis, Donatas, 2020. "Scaling transition and edge effects for negatively dependent linear random fields on Z2," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7518-7546.
    2. Surgailis, Donatas, 2024. "Scaling limits of nonlinear functions of random grain model, with application to Burgers’ equation," Stochastic Processes and their Applications, Elsevier, vol. 174(C).

    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. Surgailis, Donatas, 2020. "Scaling transition and edge effects for negatively dependent linear random fields on Z2," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7518-7546.
    2. Puplinskaitė, Donata & Surgailis, Donatas, 2015. "Scaling transition for long-range dependent Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2256-2271.
    3. Abry, Patrice & Didier, Gustavo, 2018. "Wavelet eigenvalue regression for n-variate operator fractional Brownian motion," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 75-104.
    4. Patrice Abry & Gustavo Didier & Hui Li, 2019. "Two-step wavelet-based estimation for Gaussian mixed fractional processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 157-185, July.
    5. Didier, Gustavo & Meerschaert, Mark M. & Pipiras, Vladas, 2018. "Domain and range symmetries of operator fractional Brownian fields," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 39-78.
    6. Robinson, Peter, 2019. "Spatial long memory," LSE Research Online Documents on Economics 102182, London School of Economics and Political Science, LSE Library.
    7. Surgailis, Donatas, 2024. "Scaling limits of nonlinear functions of random grain model, with application to Burgers’ equation," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    8. Lim, C.Y. & Meerschaert, M.M. & Scheffler, H.-P., 2014. "Parameter estimation for operator scaling random fields," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 172-183.
    9. Bai, Shuyang & Taqqu, Murad S. & Zhang, Ting, 2016. "A unified approach to self-normalized block sampling," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2465-2493.
    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. Beran, Jan & Ghosh, Sucharita & Schell, Dieter, 2009. "On least squares estimation for long-memory lattice processes," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2178-2194, November.
    12. Angela Ferretti & L. Ippoliti & P. Valentini & R. J. Bhansali, 2023. "Long memory conditional random fields on regular lattices," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    13. 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.
    14. Emmanuel Anyigbah & Yusheng Kong & Bless Kofi Edziah & Ahotovi Thomas Ahoto & Wilhelmina Seyome Ahiaku, 2023. "Board Characteristics and Corporate Sustainability Reporting: Evidence from Chinese Listed Companies," Sustainability, MDPI, vol. 15(4), pages 1-26, February.
    15. Valérie Mignon & Christophe Hurlin, 2007. "Une synthèse des tests de cointégration sur données de panel," Économie et Prévision, Programme National Persée, vol. 180(4), pages 241-265.
    16. Kerstin Gärtner & Mark Podolskij, 2014. "On non-standard limits of Brownian semi-stationary," CREATES Research Papers 2014-50, Department of Economics and Business Economics, Aarhus University.
    17. Yeung, Matthew C.H. & Ramasamy, Bala & Chen, Junsong & Paliwoda, Stan, 2013. "Customer satisfaction and consumer expenditure in selected European countries," International Journal of Research in Marketing, Elsevier, vol. 30(4), pages 406-416.
    18. Lee, Yoon-Jin & Okui, Ryo & Shintani, Mototsugu, 2018. "Asymptotic inference for dynamic panel estimators of infinite order autoregressive processes," Journal of Econometrics, Elsevier, vol. 204(2), pages 147-158.
    19. Chang, Yoosoon, 2004. "Bootstrap unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 120(2), pages 263-293, June.
    20. Nagmi Moftah Aimer, 2020. "Renewable energy consumption, financial development and economic growth: Evidence from panel data for the Middle East and North African countries," Economics Bulletin, AccessEcon, vol. 40(3), pages 2058-2072.

    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:127:y:2017:i:8:p:2751-2779. 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.