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Statistical methods for regular monitoring data

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  • Michael L. Stein

Abstract

Summary. Meteorological and environmental data that are collected at regular time intervals on a fixed monitoring network can be usefully studied combining ideas from multiple time series and spatial statistics, particularly when there are little or no missing data. This work investigates methods for modelling such data and ways of approximating the associated likelihood functions. Models for processes on the sphere crossed with time are emphasized, especially models that are not fully symmetric in space–time. Two approaches to obtaining such models are described. The first is to consider a rotated version of fully symmetric models for which we have explicit expressions for the covariance function. The second is based on a representation of space–time covariance functions that is spectral in just the time domain and is shown to lead to natural partially nonparametric asymmetric models on the sphere crossed with time. Various models are applied to a data set of daily winds at 11 sites in Ireland over 18 years. Spectral and space–time domain diagnostic procedures are used to assess the quality of the fits. The spectral‐in‐time modelling approach is shown to yield a good fit to many properties of the data and can be applied in a routine fashion relative to finding elaborate parametric models that describe the space–time dependences of the data about as well.

Suggested Citation

  • Michael L. Stein, 2005. "Statistical methods for regular monitoring data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 667-687, November.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:5:p:667-687
    DOI: 10.1111/j.1467-9868.2005.00520.x
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    1. Gneiting, Tilmann & Larson, Kristin & Westrick, Kenneth & Genton, Marc G. & Aldrich, Eric, 2006. "Calibrated Probabilistic Forecasting at the Stateline Wind Energy Center: The Regime-Switching SpaceTime Method," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 968-979, September.
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    Cited by:

    1. Li, Bo & Zhang, Hao, 2011. "An approach to modeling asymmetric multivariate spatial covariance structures," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1445-1453, November.
    2. 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.
    3. 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.
    4. Qianlai Zhuang & Tonglin Zhang & Jingfeng Xiao & Tianxiang Luo, 2009. "Quantification of net primary production of Chinese forest ecosystems with spatial statistical approaches," Mitigation and Adaptation Strategies for Global Change, Springer, vol. 14(1), pages 85-99, January.
    5. Indranil Sahoo & Joseph Guinness & Brian J. Reich, 2023. "Estimating atmospheric motion winds from satellite image data using space‐time drift models," Environmetrics, John Wiley & Sons, Ltd., vol. 34(8), December.
    6. 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.
    7. Christopher J. Geoga & Mihai Anitescu & Michael L. Stein, 2021. "Flexible nonstationary spatiotemporal modeling of high‐frequency monitoring data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(5), August.
    8. Shibin Zhang, 2024. "Statistical analysis of irregularly spaced spatial data in frequency domain," Journal of Time Series Analysis, Wiley Blackwell, vol. 45(5), pages 714-738, September.
    9. Soubeyrand, Samuel & Enjalbert, Jérôme & Sache, Ivan, 2008. "Accounting for roughness of circular processes: Using Gaussian random processes to model the anisotropic spread of airborne plant disease," Theoretical Population Biology, Elsevier, vol. 73(1), pages 92-103.

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