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, Volume 27, Issue 1, pp 221–245 | Cite as

Spatio-temporal analysis with short- and long-memory dependence: a state-space approach

  • Guillermo Ferreira
  • Jorge Mateu
  • Emilio Porcu
Original Paper
  • 189 Downloads

Abstract

This paper deals with the estimation and prediction problems of spatio-temporal processes by using state-space methodology. The spatio-temporal process is represented through an infinite moving average decomposition. This expansion is well known in time series analysis and can be extended straightforwardly in space–time. Such an approach allows easy implementation of the Kalman filter procedure for estimation and prediction of linear time processes exhibiting both short- and long-range dependence and a spatial dependence structure given on the locations. Furthermore, we consider a truncated state-space equation, which allows to calculate an approximate likelihood for large data sets. The performance of the proposed Kalman filter approach is evaluated by means of several Monte Carlo experiments implemented under different scenarios, and it is illustrated with two applications.

Keywords

Kalman filter algorithm Second-order stationary Space–time geostatistics Time series models 

Mathematics Subject Classification

62M10 62M20 62M30 

Notes

Acknowledgements

The first author would like to express his thanks for the support from DIUC 215.014.024-1.0, established by the Universidad de Concepción and Postdoctoral scholarship from Conicyt, Chile, 2014 (Folio 74150023). Jorge Mateu’s research was supported by Grant MTM2013-43917-P from the Spanish Ministry of Science and Education, and Grant P1-1B2015-40 and Emilio Porcu’s research was supported by Fondecyt Regular Project from Ministery of Science and Education, Chile.

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2017

Authors and Affiliations

  1. 1.Department of StatisticsUniversidad de ConcepciónConcepciónChile
  2. 2.Department of MathematicsUniversity Jaume ICastellónSpain
  3. 3.Department of MathematicsUniversity Federico Santa MaríaValparaisoChile

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