Boosting: Why You Can Use the HP Filter
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Boosting：为何可以使用 HP 滤波器
- 研究问题
- 标准 HP 滤波平滑参数可能无法充分去除随机趋势时，能否通过迭代平滑和数据决定的停止规则改进宏观序列趋势处理？
- 方法与思路
- 作者提出与 L₂ boosting 相关的迭代 HP 滤波，建立趋势恢复的极限理论，设置自动停止准则，并用三个真实数据例子展示。
- 材料陈述的贡献
- 摘要称，增强 HP 滤波能渐近恢复单位根、确定性多项式及带结构突变的多项式趋势，并适用于趋势特征不同的宏观序列。
- 阅读关注点
- 应核对迭代次数、平滑参数与样本量的关系，停止准则的理论依据，以及结构突变和高持久性下趋势恢复的适用条件。
- 阅读边界
- 所给版本为 arXiv 预印本，不能据此认定已同行评审或被期刊接收；摘要未说明停止准则细节及有限样本误差。
原文摘要
The Hodrick-Prescott (HP) filter is one of the most widely used econometric methods in applied macroeconomic research. Like all nonparametric methods, the HP filter depends critically on a tuning parameter that controls the degree of smoothing. Yet in contrast to modern nonparametric methods and applied work with these procedures, empirical practice with the HP filter almost universally relies on standard settings for the tuning parameter that have been suggested largely by experimentation with macroeconomic data and heuristic reasoning. As recent research (Phillips and Jin, 2015) has shown, standard settings may not be adequate in removing trends, particularly stochastic trends, in economic data. This paper proposes an easy-to-implement practical procedure of iterating the HP smoother that is intended to make the filter a smarter smoothing device for trend estimation and trend elimination. We call this iterated HP technique the boosted HP filter in view of its connection to $L_{2}$-boosting in machine learning. The paper develops limit theory to show that the boosted HP (bHP) filter asymptotically recovers trend mechanisms that involve unit root processes, deterministic polynomial drifts, and polynomial drifts with structural breaks. A stopping criterion is used to automate the iterative HP algorithm, making it a data-determined method that is ready for modern data-rich environments in economic research. The methodology is illustrated using three real data examples that highlight the differences between simple HP filtering, the data-determined boosted filter, and an alternative autoregressive approach. These examples show that the bHP filter is helpful in analyzing a large collection of heterogeneous macroeconomic time series that manifest various degrees of persistence, trend behavior, and volatility.