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 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.

Meteorological Time Series: An Exploratory Statistical and Critical Analysis

“…In addition, they allow incorporating covariates that are important to explain the process. In [15], they proposed a model with a state-space representation that establishes a stochastic linear relationship between the maximum temperature observed at a farm (the same database) and the h-days ahead forecast (h = 1, . .…”