IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v64y2008i3p800-806.html
   My bibliography  Save this article

A KPSS Test for Stationarity for Spatial Point Processes

Author

Listed:
  • Yongtao Guan

Abstract

Summary We propose a formal method to test stationarity for spatial point processes. The proposed test statistic is based on the integrated squared deviations of observed counts of events from their means estimated under stationarity. We show that the resulting test statistic converges in distribution to a functional of a two‐dimensional Brownian motion. To conduct the test, we compare the calculated statistic with the upper tail critical values of this functional. Our method requires only a weak dependence condition on the process but does not assume any parametric model for it. As a result, it can be applied to a wide class of spatial point process models. We study the efficacy of the test through both simulations and applications to two real data examples that were previously suspected to be nonstationary based on graphical evidence. Our test formally confirmed the suspected nonstationarity for both data.

Suggested Citation

  • Yongtao Guan, 2008. "A KPSS Test for Stationarity for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 64(3), pages 800-806, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:800-806
    DOI: 10.1111/j.1541-0420.2007.00977.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1541-0420.2007.00977.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1541-0420.2007.00977.x?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
    ---><---

    References listed on IDEAS

    as
    1. Yongtao Guan & Michael Sherman & James A. Calvin, 2006. "Assessing Isotropy for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 62(1), pages 119-125, March.
    2. Dimitris N. Politis & Michael Sherman, 2001. "Moment estimation for statistics from marked point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 261-275.
    3. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    4. Giraitis, Liudas & Leipus, Remigijus & Philippe, Anne, 2006. "A Test For Stationarity Versus Trends And Unit Roots For A Wide Class Of Dependent Errors," Econometric Theory, Cambridge University Press, vol. 22(6), pages 989-1029, December.
    5. Bart Hobijn & Philip Hans Franses & Marius Ooms, 2004. "Generalizations of the KPSS‐test for stationarity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 483-502, November.
    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. Xinyu Zhou & Wei Wu, 2024. "Statistical Depth in Spatial Point Process," Mathematics, MDPI, vol. 12(4), pages 1-20, February.
    2. Zhang, Tonglin & Zhuang, Run, 2017. "Testing proportionality between the first-order intensity functions of spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 72-82.
    3. Ka Yiu Wong & Dietrich Stoyan, 2021. "Poles of pair correlation functions: When they are real?," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 425-440, April.
    4. Yehua Li & Yongtao Guan, 2014. "Functional Principal Component Analysis of Spatiotemporal Point Processes With Applications in Disease Surveillance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1205-1215, September.
    5. Heinrich Lothar & Klein Stella, 2011. "Central limit theorem for the integrated squared error of the empirical second-order product density and goodness-of-fit tests for stationary point processes," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 359-387, December.
    6. Zhang, Tonglin & Mateu, Jorge, 2019. "Substationarity for spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 22-36.
    7. Sung Nok Chiu & Kwong Ip Liu, 2013. "Stationarity Tests for Spatial Point Processes using Discrepancies," Biometrics, The International Biometric Society, vol. 69(2), pages 497-507, June.

    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. C. Comas & F. J. Rodriguez-Cortes & J. Mateu, 2015. "Second-order analysis of anisotropic spatiotemporal point process data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 49-66, February.
    2. Jesper Møller & Håkon Toftaker, 2014. "Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 414-435, June.
    3. Edith Gabriel, 2014. "Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 411-431, June.
    4. Guan, Yongtao, 2007. "A least-squares cross-validation bandwidth selection approach in pair correlation function estimations," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1722-1729, December.
    5. Ute Hahn & Eva B. Vedel Jensen, 2016. "Hidden Second-order Stationary Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 455-475, June.
    6. Vasco Gabriel, 2003. "Tests for the Null Hypothesis of Cointegration: A Monte Carlo Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 411-435.
    7. Giuseppe Espa & Giuseppe Arbia & Diego Giuliani, 2013. "Conditional versus unconditional industrial agglomeration: disentangling spatial dependence and spatial heterogeneity in the analysis of ICT firms’ distribution in Milan," Journal of Geographical Systems, Springer, vol. 15(1), pages 31-50, January.
    8. Edith Gabriel & Peter J. Diggle, 2009. "Second‐order analysis of inhomogeneous spatio‐temporal point process data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(1), pages 43-51, February.
    9. Lüders, Erik & Lüders-Amann, Inge & Schröder, Michael, 2004. "The Power Law and Dividend Yields," ZEW Discussion Papers 04-51, ZEW - Leibniz Centre for European Economic Research.
    10. Arbia, Giuseppe & Espa, Giuseppe & Giuliani, Diego & Dickson, Maria Michela, 2014. "Spatio-temporal clustering in the pharmaceutical and medical device manufacturing industry: A geographical micro-level analysis," Regional Science and Urban Economics, Elsevier, vol. 49(C), pages 298-304.
    11. Kateřina Koňasová & Jiří Dvořák, 2021. "Stochastic Reconstruction for Inhomogeneous Point Patterns," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 527-547, June.
    12. Michaela Prokešová & Eva Jensen, 2013. "Asymptotic Palm likelihood theory for stationary point processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(2), pages 387-412, April.
    13. Redenbach, Claudia & Särkkä, Aila, 2013. "Parameter estimation for growth interaction processes using spatio-temporal information," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 672-683.
    14. Daiki Maki, 2008. "The Performance of Variance Ratio Unit Root Tests Under Nonlinear Stationary TAR and STAR Processes: Evidence from Monte Carlo Simulations and Applications," Computational Economics, Springer;Society for Computational Economics, vol. 31(1), pages 77-94, February.
    15. Saltré, F. & Chuine, I. & Brewer, S. & Gaucherel, C., 2009. "A phenomenological model without dispersal kernel to model species migration," Ecological Modelling, Elsevier, vol. 220(24), pages 3546-3554.
    16. Andersen, Torben G. & Varneskov, Rasmus T., 2021. "Consistent inference for predictive regressions in persistent economic systems," Journal of Econometrics, Elsevier, vol. 224(1), pages 215-244.
    17. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    18. Christidou, Maria & Panagiotidis, Theodore & Sharma, Abhijit, 2013. "On the stationarity of per capita carbon dioxide emissions over a century," Economic Modelling, Elsevier, vol. 33(C), pages 918-925.
    19. Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.
    20. Felix P. Hüfner & Michael Schröder, 2003. "Exchange Rate Pass-Through to Consumer Prices: A European Perspective," Aussenwirtschaft, University of St. Gallen, School of Economics and Political Science, Swiss Institute for International Economics and Applied Economics Research, vol. 58(03), pages 383-412, September.

    More about this item

    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:bla:biomet:v:64:y:2008:i:3:p:800-806. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    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.