This study introduces an innovative methodology for mortality forecasting, which integrates signature-based methods within the functional data framework of the Hyndman-Ullah (HU) model. This new approach, termed the Hyndman-Ullah with truncated signatures (HUts) model, aims to enhance the accuracy and robustness of mortality predictions. By utilizing signature regression, the HUts model is able to capture complex, nonlinear dependencies in mortality data which enhances forecasting accuracy across various demographic conditions. The model is applied to mortality data from 12 countries, comparing its forecasting performance against variants of the HU models across multiple forecast horizons. Our findings indicate that overall the HUts model not only provides more precise point forecasts but also shows robustness against data irregularities, such as those observed in countries with historical outliers. The integration of signature-based methods enables the HUts model to capture complex patterns in mortality data, making it a powerful tool for actuaries and demographers. Prediction intervals are also constructed with bootstrapping methods

翻译：本研究提出了一种创新的死亡率预测方法，该方法将基于签名的方法整合到Hyndman-Ullah（HU）模型的功能数据框架中。这种新方法被称为带截断签名的Hyndman-Ullah（HUts）模型，旨在提高死亡率预测的准确性和鲁棒性。通过利用签名回归，HUts模型能够捕捉死亡率数据中复杂的非线性依赖关系，从而在各种人口统计条件下提高预测精度。该模型应用于12个国家的死亡率数据，在多个预测时间跨度上将其预测性能与HU模型的变体进行比较。我们的研究结果表明，总体而言，HUts模型不仅提供了更精确的点预测，而且对数据不规则性（例如在具有历史异常值的国家中观察到的数据）表现出鲁棒性。基于签名的方法的整合使HUts模型能够捕捉死亡率数据中的复杂模式，使其成为精算师和人口统计学家的有力工具。预测区间也通过自助法构建。