Improving Short-term Forecasts of Daily Maximum Temperature with the Kalman Filter with GMM Estimation

Abstract

Within the scope of the TO CHAIR project, a state space modeling approach is proposed in order to improve accuracy obtained from the weatherstack.com 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 pro- duced from the website. This relation is modeled in a state space frame- work associated to the Kalman filter predictors. Since normality of dis- turbances was not a good assumption for this dataset, alternative Gen- eralized Method of Moments (GMM) estimators were considered in the models parameters estimation. The results show that this approach al- lows reducing the RMSE of the uncorrected forecasts in 16.90% consider- ing the 6-step-ahead forecasts and in 60.45% considering the 1-step-ahead forecasts, compared with the initial RMSE. Additionally, empirical con- fidence 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.