Building forecasting model for interval time series based on point series and fuzzy relationships

This study proposes a forecasting model for interval time series by splitting it into two point time series for the centroid and radius. Several important improvements have been made for each point series to obtain an effective forecasting model. First, a new series is formed by calculating the percentage change between two consecutive times. Then, the new series is divided into unequal intervals with an appropriate number found from cluster analysis technique. Fuzzy relationships between the established clusters and between each element in the series and the clusters with a normal fuzzy function are developed. Based on these relationships, a new forecasting principle for interval time series is established. The proposed model provides detailed implementation steps and is illustrated by a numerical example. Estimating confidence interval for evaluation metrics and performing Diebold -Mariano test, the proposed model demonstrates stable, competitive, and appropriate forecasting results compared to existing models, as validated on two real-world datasets of Vietnamese stock prices and temperature records. The applications have shown the potential of this study for solving two practical problems in various fields.