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Fourier analysis of irregularly spaced data on "R"-super-"d"

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  • Yasumasa Matsuda
  • Yoshihiro Yajima

Abstract

The purpose of the paper is to propose a frequency domain approach for irregularly spaced data on "R"-super-"d". We extend the original definition of a periodogram for time series to that for irregularly spaced data and define non-parametric and parametric spectral density estimators in a way that is similar to the classical approach. Introduction of the mixed asymptotics, which are one of the asymptotics for irregularly spaced data, makes it possible to provide asymptotic theories to the spectral estimators. The asymptotic result for the parametric estimator is regarded as a natural extension of the classical result for regularly spaced data to that for irregularly spaced data. Empirical studies are also included to illustrate the frequency domain approach in comparisons with the existing spatial and frequency domain approaches. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • Yasumasa Matsuda & Yoshihiro Yajima, 2009. "Fourier analysis of irregularly spaced data on "R"-super-"d"," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 191-217.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:1:p:191-217
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9868.2008.00685.x
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    References listed on IDEAS

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    1. 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.
    2. Engle, Robert F, 1974. "Band Spectrum Regression," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 1-11, February.
    3. Michael L. Stein & Zhiyi Chi & Leah J. Welty, 2004. "Approximating likelihoods for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 275-296.
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    1. repec:bla:jorssb:v:79:y:2017:i:1:p:95-123 is not listed on IDEAS
    2. repec:bla:jtsera:v:38:y:2017:i:2:p:326-351 is not listed on IDEAS
    3. Miguel A. Delgado & Peter M Robinson, 2013. "Non-Nested Testing of Spatial Correlation," STICERD - Econometrics Paper Series 568, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    4. Sam Efromovich, 2014. "Efficient Non-Parametric Estimation Of The Spectral Density In The Presence Of Missing Observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 407-427, August.
    5. Giovanna Jona Lasinio & Gianluca Mastrantonio & Alessio Pollice, 2013. "Discussing the “big n problem”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(1), pages 97-112, March.
    6. repec:cep:stiecm:/2013/568 is not listed on IDEAS
    7. Delgado, Miguel A. & Robinson, Peter M., 2013. "Non-nested testing of spatial correlation," LSE Research Online Documents on Economics 58169, London School of Economics and Political Science, LSE Library.
    8. Delgado, Miguel A. & Robinson, Peter, 2015. "Non-nested testing of spatial correlation," LSE Research Online Documents on Economics 61433, London School of Economics and Political Science, LSE Library.
    9. Delgado, Miguel A. & Robinson, Peter M., 2015. "Non-nested testing of spatial correlation," Journal of Econometrics, Elsevier, vol. 187(1), pages 385-401.
    10. Gupta, A, 2015. "Autoregressive Spatial Spectral Estimates," Economics Discussion Papers 14458, University of Essex, Department of Economics.
    11. Yasumasa Matsuda, 2013. "Generalized Whittle Estimate For Nonstationary Spatial Data," TERG Discussion Papers 305, Graduate School of Economics and Management, Tohoku University.

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