Identification of model components for a class of continuous spatiotemporal models

  • Molly I. Hartfield
  • Richard F. Gunst
Editor’s Invited Article


Environmental data routinely are collected at irregularly spaced monitoring stations and at intermittent times, times which may differ by location. This article introduces a class of continuous-time, continuous-space statistical models that can accommodate many of these more complex environmental processes. This class of models in corporates temporal and spatial variability in a cohesive manner and is broad enough to include temporal processes that are assumed to be generated by stochastic differential equations with possibly temporally and spatially correlated errors. A wide range of ARIMA temporal models and geostatistical spatial models are included in the class of models investigated. Techniques for identifying the structure of the temporal and spatial components of this class of models are detailed. Point estimates of model parameters, asymptotic distributions, and Kalman-filter prediction methods are discussed.

Key Words

ARIMA Geostatistics Intrinsic random functions Kalman filter Kriging REML Variogram 


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Copyright information

© International Biometric Society 2003

Authors and Affiliations

  • Molly I. Hartfield
    • 1
  • Richard F. Gunst
    • 2
  1. 1.Signature ScienceAustin
  2. 2.Department of Statistical ScienceSouthern Methodist UniversityDallas

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