IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v35y2014i4p357-377.html
   My bibliography  Save this article

A Frequency Domain Approach For The Estimation Of Parameters Of Spatio-Temporal Stationary Random Processes

Author

Listed:
  • Tata Subba Rao
  • Sourav Das
  • Georgi N. Boshnakov

Abstract

type="main" xml:id="jtsa12069-abs-0001"> A frequency domain methodology is proposed for estimating parameters of covariance functions of stationary spatio-temporal processes. Finite Fourier transforms of the processes are defined at each location. Based on the joint distribution of these complex valued random variables, an approximate likelihood function is constructed. The sampling properties of the estimators are investigated. It is observed that the expectation of these transforms can be considered to be a frequency domain analogue of the classical variogram. We call this measure frequency variogram. The method is applied to simulated data and also to Pacific wind speed data considered earlier by Cressie and Huang (1999). The proposed method does not depend on the distributional assumptions about the process.

Suggested Citation

  • Tata Subba Rao & Sourav Das & Georgi N. Boshnakov, 2014. "A Frequency Domain Approach For The Estimation Of Parameters Of Spatio-Temporal Stationary Random Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 357-377, July.
    • Handle: RePEc:bla:jtsera:v:35:y:2014:i:4:p:357-377
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/jtsa.12069
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Patrick E. Brown & Gareth O. Roberts & Kjetil F. Kåresen & Stefano Tonellato, 2000. "Blur‐generated non‐separable space–time models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 847-860.
    2. LI, Bo & Genton, Marc G. & Sherman, Michael, 2007. "A Nonparametric Assessment of Properties of SpaceTime Covariance Functions," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 736-744, June.
    3. Fuentes, Montserrat, 2007. "Approximate Likelihood for Large Irregularly Spaced Spatial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 321-331, March.
    4. Moreno Bevilacqua & Carlo Gaetan & Jorge Mateu & Emilio Porcu, 2012. "Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 268-280, March.
    5. Ma, Chunsheng, 2003. "Spatio-temporal stationary covariance models," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 97-107, July.
    6. John T. Kent & Mohsen Mohammadzadeh & Ali M. Mosammam, 2011. "The dimple in Gneiting's spatial-temporal covariance model," Biometrika, Biometrika Trust, vol. 98(2), pages 489-494.
    7. Yogesh Dwivedi & Suhasini Subba Rao, 2011. "A test for second‐order stationarity of a time series based on the discrete Fourier transform," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(1), pages 68-91, January.
    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. T. Subba Rao & Gyorgy Terdik, 2017. "A New Covariance Function and Spatio-Temporal Prediction (Kriging) for A Stationary Spatio-Temporal Random Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 936-959, November.
    2. Bindele, Huybrechts F., 2018. "Covariates missing at random under signed-rank inference," Econometrics and Statistics, Elsevier, vol. 8(C), pages 78-93.
    3. Huybrechts F. Bindele & Ash Abebe & Karlene N. Meyer, 2018. "General rank-based estimation for regression single index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1115-1146, October.
    4. Tata Subba Rao & Granville Tunnicliffe Wilson & Tata Subba Rao & Gyorgy Terdik, 2017. "On the Frequency Variogram and on Frequency Domain Methods for the Analysis of Spatio-Temporal Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 308-325, March.

    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. T. Subba Rao & Gyorgy Terdik, 2017. "A New Covariance Function and Spatio-Temporal Prediction (Kriging) for A Stationary Spatio-Temporal Random Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 936-959, November.
    2. Alexandre Rodrigues & Peter J. Diggle, 2010. "A Class of Convolution‐Based Models for Spatio‐Temporal Processes with Non‐Separable Covariance Structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 553-567, December.
    3. Matthias Katzfuss, 2017. "A Multi-Resolution Approximation for Massive Spatial Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 201-214, January.
    4. Harrison Quick & Sudipto Banerjee & Bradley P. Carlin, 2015. "Bayesian modeling and analysis for gradients in spatiotemporal processes," Biometrics, The International Biometric Society, vol. 71(3), pages 575-584, September.
    5. Moreno Bevilacqua & Alfredo Alegria & Daira Velandia & Emilio Porcu, 2016. "Composite Likelihood Inference for Multivariate Gaussian Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 448-469, September.
    6. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
    7. Sandra De Iaco, 2010. "Space-time correlation analysis: a comparative study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 1027-1041.
    8. Ma, Chunsheng, 2004. "Spatial autoregression and related spatio-temporal models," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 152-162, January.
    9. Giacomini, Raffaella & Granger, Clive W. J., 2004. "Aggregation of space-time processes," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 7-26.
    10. Caamaño-Carrillo, Christian & Bevilacqua, Moreno & López, Cristian & Morales-Oñate, Víctor, 2024. "Nearest neighbors weighted composite likelihood based on pairs for (non-)Gaussian massive spatial data with an application to Tukey-hh random fields estimation," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    11. Myoungji Lee & Marc G. Genton & Mikyoung Jun, 2016. "Testing Self-Similarity Through Lamperti Transformations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 426-447, September.
    12. Andrew Finley & Sudipto Banerjee & Alan Gelfand, 2012. "Bayesian dynamic modeling for large space-time datasets using Gaussian predictive processes," Journal of Geographical Systems, Springer, vol. 14(1), pages 29-47, January.
    13. Shibin Zhang, 2022. "Automatic estimation of spatial spectra via smoothing splines," Computational Statistics, Springer, vol. 37(2), pages 565-590, April.
    14. repec:esx:essedp:767 is not listed on IDEAS
    15. Montero, José-María, 2018. "Geostatistics: Unde venis et quo vadis? /Geoestadística:¿De dónde vienes y a dónde vas?," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 36, pages 81-106, Enero.
    16. Ali M. Mosammam & Jorge Mateu, 2018. "A penalized likelihood method for nonseparable space–time generalized additive models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 333-357, July.
    17. Jentsch, Carsten & Subba Rao, Suhasini, 2015. "A test for second order stationarity of a multivariate time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 124-161.
    18. Emilio Porcu & Moreno Bevilacqua & Marc G. Genton, 2016. "Spatio-Temporal Covariance and Cross-Covariance Functions of the Great Circle Distance on a Sphere," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 888-898, April.
    19. Tata Subba Rao & Granville Tunnicliffe Wilson & Tata Subba Rao & Gyorgy Terdik, 2017. "On the Frequency Variogram and on Frequency Domain Methods for the Analysis of Spatio-Temporal Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 308-325, March.
    20. 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.
    21. Francq, Christian & Zakoïan, Jean-Michel, 2022. "Testing the existence of moments for GARCH processes," Journal of Econometrics, Elsevier, vol. 227(1), pages 47-64.

    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:jtsera:v:35:y:2014:i:4:p:357-377. 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=0143-9782 .

    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.