Robust Trend Estimation for Strongly Persistent Data with Unobserved Memory

Economic analysis is often based on pre-filtered, de-trended, or seasonally adjusted data. Underlying filtering methods make strong assumptions about the memory of the series to be filtered, and inference about the memory is limited particularly when persistent cyclical variation overshadows the trend. This article introduces a data-driven method for filtering persistent series that requires no prior assumptions about the memory, thus, is robust to the actual memory of the data. It makes three primary contributions: first, it generalizes unobserved components (UC) models to fractionally integrated trends, making prior assumptions about the trend memory redundant while retaining the advantages of the state space structure of UC models; second, it establishes the asymptotic estimation theory for fractional UC models under mild assumptions; and third, it presents a computationally efficient estimator for the trend by deriving the closed-form solution to the Kalman filter optimization problem.

经济学分析通常基于预滤波、去趋势或经季节调整的数据。现有滤波方法往往对待滤波序列的记忆性施加较强假设，且当持续性周期性波动掩盖趋势时，针对序列记忆性的推断往往受限。本文提出一种面向持续性序列的数据驱动滤波方法，该方法无需预先设定关于序列记忆性的先验假设，因此对数据的实际记忆性具备鲁棒性。本文的三项主要贡献如下：其一，将不可观测成分（Unobserved Components, UC）模型推广至分整趋势场景，在保留UC模型状态空间结构优势的同时，无需再对趋势记忆性施加先验假设；其二，在温和假设条件下建立了分整UC模型的渐近估计理论；其三，通过推导卡尔曼滤波（Kalman Filter）优化问题的闭式解，给出了一种计算高效的趋势估计量。