Forecasting Using Information and Entropy Based on Belief Functions

This paper introduces an entropy-based belief function to the forecasting problem. While the likelihood-based belief function needs to know the distribution of the objective function for the prediction, the entropy-based belief function does not. This is because the observed data likelihood is somewhat complex in practice. We, thus, replace the likelihood function with the entropy. That is, we propose an approach in which a belief function is built from the entropy function. As an illustration, the proposed method is compared to the likelihood-based belief function in the simulation and empirical studies. According to the results, our approach performs well under a wide array of simulated data models and distributions. There are pieces of evidence that the prediction interval obtained from the frequentist method has a much narrower prediction interval, while our entropy-based method performs the widest. However, our entropy-based belief function still produces an acceptable range for prediction intervals as the true prediction value always lay in the prediction intervals.