Statistical methods for regular monitoring data

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. Copyright 2005 Royal Statistical Society.

[1]  Michael L. Stein,et al.  Interpolation of spatial data , 1999 .

[2]  Tony F. Chan,et al.  Circulant preconditioners for Toeplitz-block matrices , 1994, Numerical Algorithms.

[3]  Richard F. Gunst,et al.  Identification of model components for a class of continuous spatiotemporal models , 2003 .

[4]  Zhiyi Chi,et al.  Approximating likelihoods for large spatial data sets , 2004 .

[5]  N. Cressie,et al.  Classes of nonseparable, spatio-temporal stationary covariance functions , 1999 .

[6]  K. Mardia,et al.  A Bayesian kriged Kalman model for short‐term forecasting of air pollution levels , 2005 .

[7]  P. Brown,et al.  Blur‐generated non‐separable space–time models , 2000 .

[8]  George Christakos,et al.  Random Field Models in Earth Sciences , 1992 .

[9]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[10]  A. Raftery,et al.  Space-time modeling with long-memory dependence: assessing Ireland's wind-power resource. Technical report , 1987 .

[11]  P. Caines.  Linear Stochastic Systems , 1988 .

[12]  Roger Woodard,et al.  Interpolation of Spatial Data: Some Theory for Kriging , 1999, Technometrics.

[13]  Stanislav Kolenikov,et al.  Spatiotemporal modeling of PM2.5 data with missing values , 2003 .

[14]  G. Reinsel.  Elements of Multivariate Time Series Analysis , 1995 .

[15]  J. Whitaker,et al.  Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter , 2001 .

[16]  Peter Talkner,et al.  Some remarks on spatial correlation function models , 1993 .

[17]  Richard H. Jones,et al.  Models for Continuous Stationary Space-Time Processes , 1997 .

[18]  Marc G. Genton,et al.  Predictive spatio-temporal models for spatially sparse environmental data , 2005 .

[19]  Dionissios T. Hristopulos,et al.  Methods for generating non-separable spatiotemporal covariance models with potential environmental applications , 2004 .

[20]  R. J. Bennett,et al.  Spatial time series : analysis-forecasting-control , 1979 .

[21]  George Christakos,et al.  Modern Spatiotemporal Geostatistics , 2000 .

[22]  T. Gneiting.  Correlation functions for atmospheric data analysis , 1999 .

[23]  A. Yaglom.  Correlation Theory of Stationary and Related Random Functions I: Basic Results , 1987 .

[24]  A. V. Vecchia.  Estimation and model identification for continuous spatial processes , 1988 .

[25]  P. Houtekamer,et al.  A Sequential Ensemble Kalman Filter for Atmospheric Data Assimilation , 2001 .

[26]  D. E. Myers,et al.  Nonseparable Space-Time Covariance Models: Some Parametric Families , 2002 .

[27]  Nalini Ravishanker,et al.  Bayesian prediction for vector ARFIMA processes , 2002 .

[28]  T. Gneiting.  Nonseparable, Stationary Covariance Functions for Space–Time Data , 2002 .

[29]  L. Franks,et al.  Book reviews - Time series - Data analysis and theory (expanded edn.) , 1981, IEEE Communications Magazine.

[30]  S. Cohn,et al.  Ooce Note Series on Global Modeling and Data Assimilation Construction of Correlation Functions in Two and Three Dimensions and Convolution Covariance Functions , 2022 .

[31]  A. Balakrishnan,et al.  Spectral theory of random fields , 1983 .

[32]  Chunsheng Ma,et al.  Families of spatio-temporal stationary covariance models , 2003 .

[33]  I. Rodríguez‐Iturbe,et al.  Random Functions and Hydrology , 1984 .

[34]  Eric M. Aldrich,et al.  Calibrated Probabilistic Forecasting at the Stateline Wind Energy Center , 2006 .

[35]  Phaedon C. Kyriakidis,et al.  Geostatistical Space–Time Models: A Review , 1999 .

[36]  S. De Iacoa,et al.  Space – time analysis using a general product – sum model , 2000 .

[37]  D. E. Myers,et al.  The Linear Coregionalization Model and the Product–Sum Space–Time Variogram , 2003 .

[38]  M. Stein.  Space–Time Covariance Functions , 2005 .