Improving spatial temperature estimates by resort to time autoregressive processes

Abstract

Temperature estimation methods usually involve regression followed by kriging of residuals (residual kriging). Despite the performance of such models, there is invariably a residual which is not necessarily unpredictable because it may still be correlated in time. We set out to analyse such residuals through resort to autoregressive processes. It is shown that the optimal period varies depending on whether it is identified by functions of the form res d = f (res d−1 , res d−2 , . . . , res d−p ) or by partial correlations. Autoregressive processes significantly improve estimates, which are evaluated by cross-validations. Finally, the two following points are discussed: (1) the assumptions of the autoregressive model on the residuals (the assumptions of linearity, stationarity of space and time are verified empirically) and (2) the identification of the days for which the introduction of this model is really interesting.

Enhancing air quality forecasts by geomatic downscaling: an application to daily PM10 concentrations in France

“…Upon completion of the regression analysis, 325 residuals are obtained for each of the 366 days. Joly et al (2013) have shown that the application of an autoregressive process can reduce these residues. In time series such as daily PM10 concentrations, Neal et al (2014) have demonstrated that the value recorded on any day at each station is dependent on the values recorded the day before.…”