30 - 31 January 2023

Spatio-temporal modeling and prediction

Date 30 - 31 Jan 2023
Time 14:00 GMT+01:00 - 17:00 GMT+01:00
Level of instruction Intermediate
Sandra De Iaco
Claudia Cappello
Registration fee
Developed country
Developing country

Course description

Modelling spatio-temporal phenomena is a key issue in today’s research. However, the extension from pure spatial to a spatio-temporal kriging approach is not trivial. We will look into a set of different perceptions of spatio-temporal dependence and the resulting covariance models (separable, product-sum, metric, …). The practical part deals with the exploration of empirical variograms and the different variogram models applied to different data sets. Finally, some computational aspects regarding R environment and specific packages available for variogram fitting and prediction purposes will be illustrated.

Structure (1 hour per step)

  1. Step 1
    • Geostatistics and spatio-temporal random functions: theoretical framework on spatio-temporal random functions; properties of the spatio-temporal covariance function and semivariogram
    • Geostatistics and spatio-temporal random functions: an overview on some theoretical space–time covariances models
  2. Step 2
    • Introduction to different formats of spatial and spatio-temporal in R: spatio-temporal full data frame; spatio- temporal sparse data frame; spatio-temporal irregular data frame
    • Reading and writing spatial and spatio-temporal data. Subset a spatio-temporal object. Graphical representation of spatio-temporal data
  3. Step 3
    • Spatio-temporal structural analysis: semivariogram and covariogram estimation and model fitting
    • Semivariogram estimation. Fitting a spatio-temporal variogram model in R
  4. Step 4
    • Spatio-temporal structural analysis: validation and comparison of spatio-temporal semivariogram and covariogram models; some statistical tests on semivariogram and covariogram characteristics
  5. Step 5
    • Spatio-temporal prediction: spatio-temporal kriging; spatio-temporal kriging equations
    • Scripts in R to test some features of spatio-temporal covariance functions
  6. Step 6
    • Spatio-temporal interpolation in R
    • Case studies by using spatio-temporal datasets

Target audience
Statisticians interested in applications involving earth sciences

Knowledge assumed (prerequisites)
Introduction to statistics (mandatory).
Introduction to geostatistics (recommended)

Preparatory material


  • Journel, A.G. and Huijbreghts, Ch.J. 1984. Mining Geostatistics, Academic Press, London (First edition published in 1978), 600 p.
  • Hristopulos D. T. 2021. Random Fields for Spatial Data Modeling. A Primer for Scientists and Engineers, Springer, 867 p.
  • Montero JM, Fernández-Avilés G, Mateu J. 2015. Spatial and Spatio-Temporal Geostatistical Modeling and Kriging Wiley, United Kingdom
  • Sherman M, 2011. Spatial Statistics and Spatio-Temporal Data. Covariance Functions and Directional Properties. Wiley, United Kingdom
  • Cressie, N., Wikle, C., 2011. Statistics for Spatio-Temporal Data. Wiley, New Jersey, 588 p
  • Christakos, G., 2012. Modern Spatiotemporal Geostatistics. Dover Publications, Reprint edition. New York, 288 p
  • Christopher K. Wikle, Andrew Zammit-Mangion, and Noel Cressie, 2019. Spatio-Temporal Statistics with R. Chapman & Hall/CRC


  • Pebesma EJ 2020. CRAN Task View: Handling and Analyzing Spatio-Temporal Data. Version 2020-03-18, URL https://CRAN.R-project.org/view­SpatioTemporal.
  • Pebesma EJ, Bivand RS 2005. “Classes and Methods for Spatial Data in R.” R News, 5, 9–13. URL https://CRAN.R-project.org/doc/Rnews/.
  • Pebesma EJ, Bivand RS, Ribeiro PJ 2015. “Software for Spatial Statistics.” Journal of Statistical Software, 63(1). doi:10.18637/jss.v063.i01.


Sandra De Iaco is Full professor in Statistics at the University of Salento.
Sandra De Iaco

About the instructor

Affiliated with University of Salento, Italy

Sandra De Iaco is Full professor in Statistics at the University of Salento. 

Her research interests are: 

  • Space-time covariance modelling and computational aspects, 
  • Multivariate Geostatistics for environmental data, 
  • Stochastic conditional and non-conditional simulation, 
  • Multiple-point statistics,
  • Time series analysis, 
  • Multilevel regression models. 

She is an active member of the editorial board of Spatial Statistics and Mathematical Geosciences; moreover, she is reviewer for numerous international journals. She is Guest Editor of a special issue, entitled “Geostatistics and Machine Learning” in the journal Mathematical Geosciences. She participates in the scientific committees, as well as chairwoman and speaker, of the most important international conferences in the sector, aimed at welcoming new contributions in the field of spatial analysis and its various applications, including those in the environmental field. She is author of more than 140 scientific publications and 2 software packages.

Claudia-Capello is a researcher in Statistics at the University of Salento
Claudia Cappello

About the instructor

Affiliated with University of Salento, Italy

Claudia Cappello is a researcher in Statistics at the University of Salento. Her research interests are:

  • Space-time covariance modelling,
  • Multivariate Geostatistics for environmental data,
  • Computational aspects of spatial and spatio-temporal modeling and prediction