Key economic variables are often published with a significant delay of over a month. The nowcasting literature has arisen to provide fast, reliable estimates of delayed economic indicators and is closely related to filtering methods in signal processing. The path signature is a mathematical object which captures geometric properties of sequential data; it naturally handles missing data from mixed frequency and/or irregular sampling -- issues often encountered when merging multiple data sources -- by embedding the observed data in continuous time. Calculating path signatures and using them as features in models has achieved state-of-the-art results in fields such as finance, medicine, and cyber security. We look at the nowcasting problem by applying regression on signatures, a simple linear model on these nonlinear objects that we show subsumes the popular Kalman filter. We quantify the performance via a simulation exercise, and through application to nowcasting US GDP growth, where we see a lower error than a dynamic factor model based on the New York Fed staff nowcasting model. Finally we demonstrate the flexibility of this method by applying regression on signatures to nowcast weekly fuel prices using daily data. Regression on signatures is an easy-to-apply approach that allows great flexibility for data with complex sampling patterns.

翻译：关键经济变量通常延迟一个月以上才发布。即时预测文献旨在为延迟发布的经济指标提供快速可靠估计，其本质与信号处理中的滤波方法密切相关。路径特征是一种能够捕捉序列数据几何特性的数学对象——通过将观测数据嵌入连续时间域，它能自然处理混合频率和/或不规则采样带来的缺失数据问题（这在多数据源融合时尤为常见）。计算路径特征并将其作为模型特征输入，已在金融、医疗和网络安全等领域取得领先成果。本文通过路径特征回归（一种针对这些非线性对象的简单线性模型，我们证明它包含卡尔曼滤波作为特例）来研究即时预测问题。我们通过仿真实验量化其性能，并在美国GDP增速即时预测应用中看到，该方法的预测误差低于基于纽约联储工作人员即时预测模型的动态因子模型。最后，我们通过使用日度数据预测周度燃油价格，展示了路径特征回归方法的灵活性。这种方法易于实施，对具有复杂采样模式的数据具有极强的适应性。