@article{61827325742444bfb68f89c35c598dfb,
title = "Space-time autoregressive estimation and prediction with missing data based on Kalman filtering",
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.",
keywords = "autoregressive space-time model, general expectation-maximization algorithm, maximum likelihood, missing data, state-space system",
author = "Leonardo Padilla and Bernado Lagos-{\'A}lvarez and Jorge Mateu and Emilio Porcu",
note = "Funding Information: The second author thanks the VRID grant 216.014.026-1.0, from University of Concepci{\'o}n. J. Mateu has been partly granted by project MTM2016-78917-R of the Spanish government. E. Porcu is supported by Fondecyt No1170290, and by Iniciativa Cient{\'i}fica Milenio—Minecon Nucleo Milenio MESCD. Table 11 shows the values of CRVi, i=1,2,3, for the three models. We can see that for M2, the prediction quality, measured by CRV1 and CRV3 is better compared with M1 and M3. The root mean squared prediction error using M2 is smaller than for the other models, reporting an improvement of approximately 94%, by adding one more parameter to the model. Funding Information: The second author thanks the VRID grant 216.014.026‐1.0, from University of Concepci{\'o}n. J. Mateu has been partly granted by project MTM2016‐78917‐R of the Spanish government. E. Porcu is supported by Fondecyt N1170290, and by Iniciativa Cient{\'i}fica Milenio—Minecon Nucleo Milenio MESCD. o Publisher Copyright: {\textcopyright} 2020 John Wiley & Sons, Ltd.",
year = "2020",
month = nov,
day = "1",
doi = "10.1002/env.2627",
language = "British English",
volume = "31",
journal = "Environmetrics",
issn = "1180-4009",
publisher = "John Wiley and Sons Ltd",
number = "7",
}