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 (Formula presented.) is derived, and filtered series properties are studied relative to smoothing parameter ((Formula presented.)) behavior. Simulations reveal that limit theory with (Formula presented.) 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.
