标题： 使用签名方法进行实时预测 显示英文标题

标题： Nowcasting with signature methods

摘要： 关键经济变量通常会延迟超过一个月才发布。 现在预测文献的出现是为了提供延迟经济指标的快速可靠估计，这与信号处理中的滤波方法密切相关。 路径签名是一个捕捉顺序数据几何特性的数学对象；它通过将观测数据嵌入连续时间中，自然地处理来自混合频率和/或不规则采样的缺失数据——这些问题在合并多个数据源时经常遇到。 计算路径签名并将其作为模型中的特征，已在金融、医学和网络安全等领域取得了最先进的结果。 我们通过在签名上应用回归来研究现在预测问题，这是一种针对这些非线性对象的简单线性模型，我们证明它涵盖了流行的卡尔曼滤波器。 我们通过模拟练习量化性能，并通过应用于现在预测美国GDP增长，其中我们看到比基于纽约联储工作人员现在预测模型的动态因子模型误差更低。 最后，我们通过在签名上应用回归来现在预测每周燃油价格，使用每日数据，展示了该方法的灵活性。 在签名上进行回归是一种易于应用的方法，允许具有复杂采样模式的数据有极大的灵活性。 显示英文摘要

摘要： 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.