IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/58100.html
   My bibliography  Save this paper

Inference on power law spatial trends (Running Title: Power Law Trends)

Author

Listed:
  • Robinson, Peter M.

Abstract

Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space-time. Consistency and asymptotic normality of nonlinear least squares estimates of the parameters are established. The joint limit distribution is singular, but can be used as a basis for inference on either exponents or coefficients. We discuss issues of implementation, efficiency, potential for improved estimation, and possibilities of extension to more general or alternative trending models, and to allow for irregularlyspaced data or heteroscedastic errors; though it focusses on a particular model to .x ideas, the paper can be viewed as offering machinery useful in developing inference for a variety of models in which power law trends are a component. Indeed, the paper also makes a contribution that is potentially relevant to many other statistical models: our problem is one of many in which consistency of a vector of parameter estimates (which converge at different rates) cannot be established by the usual techniques for coping with implicitlydefined extremum estimates, but requires a more delicate treatment; we present a generic consistency result.J

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:58100
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/58100/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lu, Zudi & Lundervold, Arvid & Tjøstheim, Dag & Yao, Qiwei, 2007. "Exploring spatial nonlinearity using additive approximation," LSE Research Online Documents on Economics 5401, London School of Economics and Political Science, LSE Library.
    2. 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.
    3. Yoshihiro Yajima & Yasumasa Matsuda, 2008. "Asymptotic Properties of the LSE of a Spatial Regression in both Weakly and Strongly Dependent Stationary Random Fields," CIRJE F-Series CIRJE-F-587, CIRJE, Faculty of Economics, University of Tokyo.
    4. 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.
    5. Nielsen, Morten Orregaard, 2007. "Local Whittle Analysis of Stationary Fractional Cointegration and the ImpliedRealized Volatility Relation," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 427-446, October.
    6. Giraitis, L & Hidalgo, J & Robinson, Peter M., 2001. "Gaussian estimation of parametric spectral density with unknown pole," LSE Research Online Documents on Economics 297, London School of Economics and Political Science, LSE Library.
    7. Giraitis, Liudas & Hidalgo, Javier & Robinson, Peter, 2001. "Gaussian estimation of parametric spectral density with unknown pole," LSE Research Online Documents on Economics 2182, London School of Economics and Political Science, LSE Library.
    8. Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models. I. Time series," LSE Research Online Documents on Economics 57580, London School of Economics and Political Science, LSE Library.
    9. Sun, Yixiao & Phillips, Peter C. B., 2003. "Nonlinear log-periodogram regression for perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 115(2), pages 355-389, August.
    10. Qiwei Yao & Peter J. Brockwell, 2006. "Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 857-875, November.
    11. Liudas Giraitis & Javier Hidalgo & Peter M Robinson, 2001. "Gaussian Estimation of Parametric Spectral Density with Unknown Pole," STICERD - Econometrics Paper Series 424, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    12. Marc Hallin & Zudi Lu & Lanh T. Tran, 2001. "Density estimation for spatial linear processes," ULB Institutional Repository 2013/2109, ULB -- Universite Libre de Bruxelles.
    13. Yao, Qiwei & Brockwell, Peter J., 2006. "Gaussian maximum likelihood estimation for ARMA models I: time series," LSE Research Online Documents on Economics 5825, London School of Economics and Political Science, LSE Library.
    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. Peter M Robinson, 2011. "Inference on Power Law Spatial Trends (Running Title: Power Law Trends)," STICERD - Econometrics Paper Series 556, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. repec:cep:stiecm:/2011/556 is not listed on IDEAS
    3. 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.
    4. Robinson, P.M., 2011. "Asymptotic theory for nonparametric regression with spatial data," Journal of Econometrics, Elsevier, vol. 165(1), pages 5-19.
    5. repec:esx:essedp:767 is not listed on IDEAS
    6. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    7. Tianhao Wang & Yingcun Xia, 2015. "Whittle Likelihood Estimation of Nonlinear Autoregressive Models With Moving Average Residuals," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1083-1099, September.
    8. Zheng, Tingguo & Chen, Rong, 2017. "Dirichlet ARMA models for compositional time series," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 31-46.
    9. 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.
    10. Dimitriou-Fakalou, Chrysoula, 2019. "On accepting the edge-effect (for the inference of ARMA-type processes in Z2)," Econometrics and Statistics, Elsevier, vol. 10(C), pages 53-70.
    11. Hassler, Uwe, 2011. "Estimation of fractional integration under temporal aggregation," Journal of Econometrics, Elsevier, vol. 162(2), pages 240-247, June.
    12. Hernández, Juan R., 2016. "Unit Root Testing in ARMA Models: A Likelihood Ratio Approach," MPRA Paper 100857, University Library of Munich, Germany.
    13. Huang, Lei & Jiang, Hui & Wang, Huixia, 2019. "A novel partial-linear single-index model for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 110-122.
    14. Dimitriou-Fakalou, Chrysoula, 2009. "Modified Gaussian likelihood estimators for ARMA models on," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4149-4175, December.
    15. Mélard, Guy, 2022. "An indirect proof for the asymptotic properties of VARMA model estimators," Econometrics and Statistics, Elsevier, vol. 21(C), pages 96-111.
    16. Tingjin Chu & Jialuo Liu & Jun Zhu & Haonan Wang, 2022. "Spatio-Temporal Expanding Distance Asymptotic Framework for Locally Stationary Processes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 689-713, August.
    17. 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.
    18. Yong Bao, 2018. "The asymptotic covariance matrix of the QMLE in ARMA models," Econometric Reviews, Taylor & Francis Journals, vol. 37(4), pages 309-324, April.
    19. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    20. Qin Shao & Lijian Yang, 2017. "Oracally efficient estimation and consistent model selection for auto-regressive moving average time series with trend," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 507-524, March.
    21. Norkutė, Milda & Westerlund, Joakim, 2019. "The factor analytical method for interactive effects dynamic panel models with moving average errors," Econometrics and Statistics, Elsevier, vol. 11(C), pages 83-104.
    22. Abdelkamel Alj & Rajae Azrak & Christophe Ley & Guy Mélard, 2017. "Asymptotic Properties of QML Estimators for VARMA Models with Time-dependent Coefficients," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 617-635, September.

    More about this item

    Keywords

    asymptotic normality; consistency; correlation; generalized polynomial; lattice; power law.0Út;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

    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:ehl:lserod:58100. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.