The design of weather index insurance from a risk reduction perspective：Asequential residual learning algorithm

This study aims to design a weather index insurance product featuring dynamic payout throughout the entire growth cycle of crops. The product is intended to respond promptly to adverse weather conditions at different growth stages, provide rapid compensation, and convert insurance payouts into funds for disaster prevention and loss reduction. This approach supports and encourages farmers to take proactive measures in mitigating risks. Using county-level yield data of winter wheat from Hebei, Shandong, and Henan provinces (1990—2022) along with meteorological data, this study leverages the concept of residual learning from gradient boosting algorithms. The entire growth period of winter wheat is divided into five stages, and 16 meteorological indicators—such as temperature, precipitation, and wind speed are selected. A random forest-sequential method is employed to predict yield loss at each growth stage. Starting from the second stage, the residual from the previous stage's prediction is used as the target variable for modeling. Payouts are triggered whenever the predicted loss at any stage exceeds a predefined threshold. Multiple meteorological factors are found to influence winter wheat yield, with their impacts varying by growth stage and depending on the intensity and duration of weather conditions. Relying on a single indicator or a single growth stage is proved to be insufficient for accurately assessing final yield loss. The random forest-sequential method demonstrates strong out-of-sample predictive performance, effectively capturing the complex relationship between weather and yield. It outperforms both multiple linear regression and non-sequential random forest approaches, particularly in predicting large yield losses. When relatively severe yield losses occur, the proposed insurance product provides effective compensation. However, a certain degree of basis risk remains, especially in cases of minimal or no actual loss, where payouts could still be triggered. The algorithm based on sequential residual learning offers an effective means of predicting yield loss. By assessing risks stage by stage throughout the crop growth cycle, this method ensures timely payouts and enables early- to mid-season financial support for farmers, facilitating proactive disaster prevention and loss reduction.