Identification of model components for a class of continuous spatiotemporal models
- 63 Downloads
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 WordsARIMA Geostatistics Intrinsic random functions Kalman filter Kriging REML Variogram
Unable to display preview. Download preview PDF.
- Bennet, R. J. (1974), “The Representation and Identification of Spatio-Temporal Systems: An Example of Population Diffusion in North-west England,” Transactions and Papers of the Institute of British Geographers, 66, 73–94.Google Scholar
- Cavanagh, C. L., and Rothenberg, T. J. (1995), “Generalized Least Squares with Nonnormal Errors,” in Advances in Econometrics and Quantitative Economics, eds. G. S. Maddala, P. C. B. Phillips, and T. N. Srinivasan, Cambridge, MA: Basil Blackwell.Google Scholar
- Cliff, A. D., and Ord, J. K. (1974), “Space-Time Modeling With an Application to Regional Forecasting,” Transactions and Papers of the Institute of British Geographers, 66, 119–128.Google Scholar
- — (1993), Statistics for Spatial Data (revised edition), New York: Wiley.Google Scholar
- Guttorp, P., Sampson, P. D., and Newman, K. (1992), “Nonparametric Estimation of Spatial Covariance With Application to Monitoring Network Evaluation,” in Statistics in the Environmental and Earth Sciences, eds. A. T. Walder and P. Guttorp, London: Charles W. Griffin.Google Scholar
- Journel, A. G., and Huijbregts, C. J. (1978), Mining Geostatistics, New York: Academic Press.Google Scholar
- Loader, C., and Switzer, P. (1992), “Spatial Covariance Estimation for Monitoring Data,” in Statistics in the Environmental and Earth Sciences, eds. A. T. Walder and P. Guttorp. London: Charles W. Griffin.Google Scholar
- Rouhani, S., Ebrahimpour, M. R., Yaqub, L., and Gianella, E. (1992), “Multivariate Geostatistical Trend Detection and Network Evaluation of Space-Time Acid Deposition Data—1. Methodology,” Atmospheric Environment, 26A, 2603–2614.Google Scholar
- Rouhani, S., and Hall, T. J. (1989), “Space-Time Kriging of Groundwater Data,” Geostatistics (vol. 2), ed. M. Armstrong, New York: Kluwer.Google Scholar