On the Model-Based Interpretation of Filters and the Reliability of Trend–Cycle Estimates
研究经济时间序列中趋势和周期测量滤波器的设计权衡，特别是估计可靠性与修正幅度之间的基本矛盾，通过一种新的基于模型的方法将HP滤波器等适配到特定序列，并利用ARIMA分解和卡尔曼滤波进行最优估计。
The article explores and illustrates some of the typical trade-offs which arise in designing filters for the measurement of trends and cycles in economic time series, focusing, in particular, on the fundamental trade-off between the reliability of the estimates and the magnitude of the revisions as new observations become available. This assessment is available through a novel model based approach, according to which an important class of highpass and bandpass filters, encompassing the Hodrick–Prescott (HP) filter, are adapted to the particular time series under investigation. Via a suitable decomposition of the innovation process, it is shown that any linear time series with ARIMA representation can be broken down into orthogonal trend and cycle components, for which the class of filters is optimal. The main results then follow from Wiener–Kolmogorov (WK) signal extraction theory, whereas exact finite sample inferences are provided by the Kalman filter and smoother for the relevant state space representation of the decomposition.