Filtering economic time series: On the cyclical properties of Hamilton's regression filter and the Hodrick-Prescott filter
比较汉密尔顿滤波和霍德里克-普雷斯科特滤波的周期性质，发现汉密尔顿滤波在避免HP滤波缺陷的同时，会引入相位偏移和方差改变，且这些影响因时间序列而异。
The Hamilton (H) filter is proposed as an alternative to the Hodrick-Prescott (HP) filter. It is designed to meet all of the objectives desired by users of the HP filter while avoiding its drawbacks (spurious dynamics, ad hoc filter settings, end-of-sample bias). I document a trade-off that has been overlooked: Addressing the HP filter's drawbacks means that the H filter cannot fulfill all of the desired objectives. It modifies different frequencies captured in an estimated cyclical component by inducing phase shifts and by likely altering variances. Typically, these modifications vary across time series. Through both simulation and real data exercises, I illustrate each filter's cyclical properties.