Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry

Abstract

Geostatistical approaches to modeling spatio-temporal data rely on parametric covariance models and rather stringent assumptions, such as stationarity, separability and full symmetry. This paper reviews recent advances in the literature on space-time covariance functions in light of the aforementioned notions, which are illustrated using wind data from Ireland. Experiments with time-forward kriging predictors suggest that the use of more complex and more realistic covariance models results in improved predictive performance.

Spatio-Temporal Covariance Modeling With Some Arma Temporal Margins

“…To compare the proposed model (3) with existing models presented by Gneiting (2002), Gneiting et al (2007). We use the Irish wind data set first analyzed by Haslett and Raftery (1989).…”

“…Here we use the existing parameter estimates that we found in the symmetric case and use weighted least squares and obtain fitted estimates λ = 234 kilometers per day and v = 0.0573 as did in Gneiting et al (2007).…”

“…This is a spatio-temporal data set that measures average daily wind speeds taken from twelve synoptic meteorological weather stations in Ireland from year 1961 to 1978. As in Haslett and Raftery (1989), Gneiting (2002), Gneiting et al (2007) and Stein (2005aStein ( , 2005b, the following steps were taken to clean the data. A square root transformation is taken to stabilize the variance over both stations and time periods so that the margins of space and time to be approximately normally distributed.…”

“…The proposed model is given in next section and its related proof is postponed to the appendix. In Section 4, the proposed model is fitted to Irish wind data and the results are presented by comparing with those using the model developed by Gneiting (2002), and Gneiting et al (2007) in both symmetric and asymmetric cases.…”

The dimple in Gneiting's spatial-temporal covariance model

“…Choice Function Parameter 1 ψ(w) = (w + 1) β 0 ≤ β ≤ 1 2 ψ(w) = log(w + b)/ log(b) b > 1 models proposed by Gneiting (2002) and Gneiting et al (2007), and building on Cressie and Huang (1999), takes the form…”