IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i10p2178-2194.html
   My bibliography  Save this article

On least squares estimation for long-memory lattice processes

Author

Listed:
  • Beran, Jan
  • Ghosh, Sucharita
  • Schell, Dieter

Abstract

A flexible class of anisotropic stationary lattice processes with long memory can be defined in terms of a two-way fractional ARIMA (FARIMA) representation. We consider parameter estimation based on minimizing an approximate residual sum of squares. The method can be applied to sampling areas that are not necessarily rectangular. A central limit theorem is derived under general conditions. The method is illustrated by an analysis of satellite data consisting of total column ozone amounts in Europe and the Atlantic respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:10:p:2178-2194
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00085-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Sain, Stephan R. & Cressie, Noel, 2007. "A spatial model for multivariate lattice data," Journal of Econometrics, Elsevier, vol. 140(1), pages 226-259, September.
    2. Jeremy Smith & Nick Taylor & Sanjay Yadav, 1997. "Comparing the bias and misspecification in ARFIMA models," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(5), pages 507-527, September.
    3. 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.
    4. Paul Doukhan & Patrice Bertail & Philippe Soulier, 2006. "Dependence in Probability and Statistics," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00268232, HAL.
    5. Robinson, P.M. & Vidal Sanz, J., 2006. "Modified Whittle estimation of multilateral models on a lattice," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1090-1120, May.
    6. E. Moulines & F. Roueff & M. S. Taqqu, 2007. "On the Spectral Density of the Wavelet Coefficients of Long‐Memory Time Series with Application to the Log‐Regression Estimation of the Memory Parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 155-187, March.
    7. Heyde, C. C. & Gay, R., 1993. "Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 169-182, March.
    8. 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.
    9. Paul Doukhan & Patrice Bertail & Philippe Soulier, 2006. "Dependence in Probability and Statistics," Post-Print hal-00268232, HAL.
    10. Cheung, Yin-Wong & Diebold, Francis X., 1994. "On maximum likelihood estimation of the differencing parameter of fractionally-integrated noise with unknown mean," Journal of Econometrics, Elsevier, vol. 62(2), pages 301-316, June.
    11. Ruiz-Medina, M. D. & Angulo, J. M. & Anh, V. V., 2003. "Fractional-order regularization and wavelet approximation to the inverse estimation problem for random fields," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 192-216, April.
    12. Fernández-Pascual, Rosaura & Ruiz-Medina, María D. & Angulo, José M., 2006. "Estimation of intrinsic processes affected by additive fractal noise," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1361-1381, July.
    13. Laura Mayoral, 2007. "Minimum distance estimation of stationary and non-stationary ARFIMA processes," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 124-148, March.
    14. Lieberman, Offer & Rousseau, Judith & Zucker, David M., 2000. "Small-Sample Likelihood-Based Inference In The Arfima Model," Econometric Theory, Cambridge University Press, vol. 16(2), pages 231-248, April.
    15. Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models II: spatial processes," LSE Research Online Documents on Economics 5416, London School of Economics and Political Science, LSE Library.
    16. Giraitis, L. & Robinson, P.M., 2003. "Edgeworth expansions for semiparametric Whittle estimation of long memory," LSE Research Online Documents on Economics 291, London School of Economics and Political Science, LSE Library.
    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. Nikolai Leonenko & Andriy Olenko, 2013. "Tauberian and Abelian Theorems for Long-range Dependent Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 715-742, December.
    2. Robinson, Peter, 2019. "Spatial long memory," LSE Research Online Documents on Economics 102182, London School of Economics and Political Science, LSE Library.
    3. 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.
    4. Bastian Schäfer, 2021. "Bandwidth selection for the Local Polynomial Double Conditional Smoothing under Spatial ARMA Errors," Working Papers CIE 146, Paderborn University, CIE Center for International Economics.
    5. Otto, Philipp & Sibbertsen, Philipp, 2023. "Spatial autoregressive fractionally integrated moving average model," Hannover Economic Papers (HEP) dp-712, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    6. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.
    7. 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.

    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. Robinson, Peter, 2019. "Spatial long memory," LSE Research Online Documents on Economics 102182, London School of Economics and Political Science, LSE Library.
    2. Rosa Espejo & Nikolai Leonenko & Andriy Olenko & María Ruiz-Medina, 2015. "On a class of minimum contrast estimators for Gegenbauer random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 657-680, December.
    3. repec:esx:essedp:767 is not listed on IDEAS
    4. 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.
    5. Anh, V.V. & Leonenko, N.N. & Sakhno, L.M., 2007. "Statistical inference using higher-order information," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 706-742, April.
    6. Nikolai Leonenko & Andriy Olenko, 2013. "Tauberian and Abelian Theorems for Long-range Dependent Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 715-742, December.
    7. Gadea, Maria Dolores & Sabate, Marcela & Serrano, Jose Maria, 2004. "Structural breaks and their trace in the memory: Inflation rate series in the long-run," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 14(2), pages 117-134, April.
    8. Klar, B. & Lindner, F. & Meintanis, S.G., 2012. "Specification tests for the error distribution in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3587-3598.
    9. Ahmed BenSaïda, 2021. "The Good and Bad Volatility: A New Class of Asymmetric Heteroskedastic Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(2), pages 540-570, April.
    10. Salaheddine El Adlouni, 2018. "Quantile regression C-vine copula model for spatial extremes," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(1), pages 299-317, October.
    11. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    12. Ana Pérez & Esther Ruiz, 2002. "Modelos de memoria larga para series económicas y financieras," Investigaciones Economicas, Fundación SEPI, vol. 26(3), pages 395-445, September.
    13. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    14. Lihong Wang & Jinde Wang, 2014. "Wavelet estimation of the memory parameter for long range dependent random fields," Statistical Papers, Springer, vol. 55(4), pages 1145-1158, November.
    15. Bertail, Patrice & Clemencon, Stephan, 2008. "Approximate regenerative-block bootstrap for Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2739-2756, January.
    16. Stelios Arvanitis & Antonis Demos, 2015. "A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 200-241, June.
    17. 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.
    18. Christian FRANCQ & Jean-Michel ZAKOIAN, 2009. "Properties of the QMLE and the Weighted LSE for LARCH(q) Models," Working Papers 2009-19, Center for Research in Economics and Statistics.
    19. Stoyan V. Stoyanov & Svetlozar T. Rachev & Stefan Mittnik & Frank J. Fabozzi, 2019. "Pricing Derivatives In Hermite Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-27, September.
    20. Robinson, Peter M., 2011. "Inference on power law spatial trends (Running Title: Power Law Trends)," LSE Research Online Documents on Economics 58100, London School of Economics and Political Science, LSE Library.
    21. Paul Doukhan & Jean-David Fermanian & Gabriel Lang, 2009. "An empirical central limit theorem with applications to copulas under weak dependence," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 65-87, February.

    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:100:y:2009:i:10:p:2178-2194. 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.