Improving short-term forecasts of daily maximum temperature with the Kalman filter with GMM estimation

Within the scope of the TO CHAIR project, a state space modeling approach is proposed in order to improve accuracy obtained from the weatherstack. corn website with a dataset of real observations. The proposed model establishes a stochastic linear relationship between the maximum temperature observed and the h-step-ahead forecast produced from the website. This relation is modeled in a state space framework associated to the Kalman filter predictors. Since normality of disturbances was not a good assumption for this dataset, alternative Generalized Method of Moments (GMM) estimators were considered in the models parameters estimation. The results show that this approach allows reducing the RMSE of the uncorrected forecasts in 16.90% considering the 6-step-ahead forecasts and in 60.45% considering the 1-step-ahead forecasts, compared with the initial RMSE. Additionally, empirical confidence intervals at the 95% level have a coverage rate similar to this confidence level. So, this approach has proven suitable for this type of forecasts correction since it considers a stochastic calibration factor in order to model time correlation of this type of variable. ; - This work has received funding from FEDER/COMPETE/NORTE2020/POCI/FCT funds through grants UID/EEA/-00147/20 13/UID/IEEA/00147/006933-SYSTEC, project and To CHAIR -POCI-01-0145-FEDER-028247. This work was also partially supported by the Portuguese FCT Projects UIDB/00013/2020 and UIDP/00013/2020 of CMAT-UM and the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT - Fundacao para a Ciencia e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020.