The Band Pass Filter
为带通滤波器开发了最优有限样本近似，包括可用于实时分析的单边滤波器，并发现基于随机游走的简单近似对宏观经济数据几乎最优，同时揭示了1960年前后货币与通胀关系的显著变化。
We develop optimal finite‐sample approximations for the band pass filter. These approximations include one‐sided filters that can be used in real time. Optimal approximations depend upon the details of the time series representation that generates the data. Fortunately, for U.S. macroeconomic data, getting the details exactly right is not crucial. A simple approach, based on the generally false assumption that the data are generated by a random walk, is nearly optimal. We use the tools discussed here to document a new fact: There has been a significant shift in the money–inflation relationship before and after 1960.