Hodrick-Prescott Filter

The Hodrick-Prescott (HP) filter is a specialized filter for trend and business cycle estimation (no seasonal component). Suppose a time seriesy_tcan be additively decomposed into a trend and business cycle component. Denote the trend componentg_tand the cycle componentc_t. Then $$y_t=g_t+c_t.$$

The HP filter finds a trend estimate, $${\hat{g}}_t$$, by solving a penalized optimization problem. The smoothness of the trend estimate depends on the choice of penalty parameter. The cycle component, which is often of interest to business cycle analysts, is estimated as $${\hat{c}}_t=y_t-{\hat{g}}_t$$.

hpfilter返回估计趋势和周期分量of a time series.

See Also

hpfilter

Related Examples

• Using the Hodrick-Prescott Filter to Reproduce Their Original Result

More About

• Moving Average Filter
• Seasonal Filters
• Time Series Decomposition