BUSINESS CYCLES, TREND ELIMINATION, AND THE HP FILTER
用有限样本和渐近方法分析HP滤波在消除趋势和估计经济周期中的表现，发现其无法去除随机趋势，导致虚假周期，并联系全球金融危机的长期影响。
Abstract Trend elimination and business cycle estimation are analyzed by finite sample and asymptotic methods. An overview history is provided, operator theory is developed, limit theory as the sample size is derived, and filtered series properties are studied relative to smoothing parameter ( ) behavior. Simulations reveal that limit theory with delivers excellent approximations to the HP filter for common sample sizes but fails to remove stochastic trends, contrary to standard thinking in macroeconomics and thereby explaining “spurious cycle” effects of the HP filter. The findings are related to the long run effects of the global financial crisis.