Spatio-temporal analysis with short- and long-memory dependence: a state-space approach
- 189 Downloads
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.
KeywordsKalman filter algorithm Second-order stationary Space–time geostatistics Time series models
Mathematics Subject Classification62M10 62M20 62M30
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.
- Bivand R, Keitt T, Rowlingson B (2015) rgdal: bindings for the geospatial data abstraction library. R Foundation for Statistical Computing, ViennaGoogle Scholar
- Bocquet M, Elbern H, Eskes H, Hirtl M, Zabkar R, Carmichael G, Flemming J, Inness A, Pagowski M, Pérez Camaño J et al (2015) Data assimilation in atmospheric chemistry models: current status and future prospects for coupled chemistry meteorology models. Atmos Chem Phys 15(10):5325–5358CrossRefGoogle Scholar
- Broyden CG (1969) A new double-rank minimization algorithm. Not Am Math Soc 16:670Google Scholar
- Harvey AC (1989) Forecasting structural time series and the Kalman filter. Cambridge University Press, CambridgeGoogle Scholar
- Haslett J, Raftery AE (1989) Space–time modelling with long-memory dependence: assessing Ireland’s wind power resource. J R Stat Soc C Appl 38(1):1–50Google Scholar
- Matérn B (1986) Spatial variation, volume 36 of lecture notes in statistics. Springer, BerlinGoogle Scholar
- Peng RD, de Leeuw J (2002) An introduction to the .C interface to R. UCLA, Academic Technology Services, Statistical Consulting GroupGoogle Scholar
- R Core Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
- Zes D (2014) Facile spatio-temporal modeling, forecasting with adaptive least squares and the Kalman filter. J Environ Stat 6(1). http://jes.stat.ucla.edu/v06/i01