Universal kriging of functional data: trace-variography vs cross-variography? Application to forecasting in unconventional shales

In this paper we investigate the practical and methodological use of Universal Kriging of functional data to predict unconventional shale gas production in undrilled locations from known production data. In Universal Kriging of functional data, two approaches are considered: (1) estimation by means of Cokriging of functional components (Universal Cokriging, UCok), requiring cross-variography and (2) estimation by means of trace-variography (Universal Trace-Kriging, UTrK), which avoids cross-variogram modeling. While theoretically, under known variogram structures, such approaches may be quite equivalent, their practical application implies different estimation procedures and modeling efforts. We investigate these differences from the methodological viewpoint and by means of a real field application in the Barnett shale play. An extensive Monte Carlo study inspired from such real field application is employed to support our conclusions.