Graduate School of Engineering
Kyushu University
Research Skills
Universal spatio-temporal kriging
■ Kriging
Kriging is a method for spatial interpolation developed in the field of geostatistics. Under the assumption of second-order stationary in a random field, a value at any point in the domain is predictable using a characteristic that the spatially closer observation points have larger similarities. For the details in the theory of kriging, see Cressie (1993) and Wackernagel (1995). Universal kriging is a type of kriging that interpolates based on a covariance function structuralized from OLS residuals. This method originates from the best linear unbiased predictor (BLUP). Spatio-temporal kriging is an extension whose random field includes time dimension as well as space (Bilonick 1988; Cressie 1993; Cressie and Huang 1999; Gneiting 2002; Snepvangers et al. 2003). Modeling both spatial and temporal structures of observations, spatio-temporal kriging provides superior estimators to conventional kriging. Although the theory and methodology of kriging are developed in the fields of natural science, some studies apply kriging for real estate analysis (Basu and Thibodeau 1998; Dubin 1998; Inoue et al. 2009; Tsutsumi et al. 2014; Morales et al. 2020).
■ Methodology
A structure of spatio-temporal is characterized by a semi-variogram. In universal kriging, a semi-variogram depends on the magnitude of regression residuals. The longer distance (x-axis), the greater value of gamma (y-axis). Spatio-temporal kriging extends to a temporal domain as well as a spatial domain.
Author
■ The effectiveness of kriging
To visualize the effectiveness of universal spatio-temporal kriging for creating a panel dataset, we take land prices as an example (see the figure below). First, we calculate the conventional land prices of each block, called the non-kriging model (b). There are 274 blocks in total. after omitting inconsistent boundaries through the period. However, the non-kriging model has only 60 blocks with average land prices. Second, we calculate area-weighted average land prices based on the kriging, called the kriging model (d). Unlike the non-kriging model, the kriging model allows us to obtain values in all 274 blocks.
