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Space‐time autoregressive estimation and prediction with missing data based on Kalman filtering

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  • Leonardo Padilla
  • Bernado Lagos‐Álvarez
  • Jorge Mateu
  • Emilio Porcu

Abstract

We propose a Kalman filter algorithm to provide a formal statistical analysis of space‐time data with an autoregressive structure in time. The Kalman filter technique allows to capture the temporal dependence as well as the spatial correlation structure through state‐space equations, and it is aimed to perform statistical inference in terms of parameter estimation and prediction at unobserved locations. We thus develop space‐time estimation and prediction methods in the presence of missing data, through the Kalman filter, in order to obtain accurate estimates of model parameters and reliable space‐time predictions. Our findings are illustrated through an application on daily air temperatures in some regions of southern Chile, where the dataset shows a number of missing data in many locations.

Suggested Citation

  • Leonardo Padilla & Bernado Lagos‐Álvarez & Jorge Mateu & Emilio Porcu, 2020. "Space‐time autoregressive estimation and prediction with missing data based on Kalman filtering," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
    • Handle: RePEc:wly:envmet:v:31:y:2020:i:7:n:e2627
    DOI: 10.1002/env.2627
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    1. Michela Cameletti & Finn Lindgren & Daniel Simpson & Håvard Rue, 2013. "Spatio-temporal modeling of particulate matter concentration through the SPDE approach," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(2), pages 109-131, April.
    2. Kwong, Koon-Shing & Iglewicz, Boris, 1996. "On singular multivariate normal distribution and its applications," Computational Statistics & Data Analysis, Elsevier, vol. 22(3), pages 271-285, July.
    3. Wenceslao González‐Manteiga & Rosa M. Crujeiras & Matthias Katzfuss & Noel Cressie, 2012. "Bayesian hierarchical spatio‐temporal smoothing for very large datasets," Environmetrics, John Wiley & Sons, Ltd., vol. 23(1), pages 94-107, February.
    4. Huang, Hsin-Cheng & Cressie, Noel, 1996. "Spatio-temporal prediction of snow water equivalent using the Kalman filter," Computational Statistics & Data Analysis, Elsevier, vol. 22(2), pages 159-175, July.
    5. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    6. Crescenza Calculli & Alessandro Fassò & Francesco Finazzi & Alessio Pollice & Annarita Turnone, 2015. "Maximum likelihood estimation of the multivariate hidden dynamic geostatistical model with application to air quality in Apulia, Italy," Environmetrics, John Wiley & Sons, Ltd., vol. 26(6), pages 406-417, September.
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