A functional time series approach is proposed for investigating spatial correlation in daily maximum temperature forecast errors for 111 cities spread across the U.S. The modelling of spatial correla- tion is most fruitful for longer forecast horizons, and becomes less relevant as the forecast horizon shrinks towards zero. For 6-day-ahead forecasts, the functional approach uncovers interpretable re- gional spatial effects, and captures the higher variance observed in inland cities vs. coastal cities, as well as the higher variance observed in mountain and midwest states. The functional approach also naturally handles missing data through modelling a continuum, and can be implemented efficiently by exploiting the sparsity induced by a B-spline basis.
The temporal dependence in the data is well-characterized by AR(1)-GARCH(1,1) processes with Student-t innovations, which capture the persistence of basis coefficients over time and the seasonal heteroskedasticity reflecting higher variance in winter. Through exploiting autocorrelation in the basis coefficients, the functional time series approach also suggests a method for improving weather forecasts and uncertainty quantification.