Interpolation and linear prediction of data -- three kernel selection criteria

Interpolation and prediction have been useful approaches in modeling data in many areas of applications. The aim of this paper is the prediction of the next value of a time series (time series forecasting) using the techniques in interpolation of the spatial data, for the tow approaches kernel interpolation and kriging. We are interested in finding some sufficient conditions for the kernels and provide a detailed analyse of the prediction using kernel interpolation. Finally, we provide a natural idea to select a good kernel among a given family of kernels using only the data. We illustrate our results by application to the data set on the mean annual temperature of France and Morocco recorded for a period of 115 years (1901 to 2015).