Analysis of macroeconomic time series by the HP filter

This paper analyzes the transmission characteristics of the Hodrick-Prescott (HP) filter and frequency characteristics of exponential series, defines 3dB bandwidths of both the HP filter and exponential time series. Formulas of the 3dB bandwidths of the HP filter and exponential time series are derived. Thus, a method to determine the smoothing parameters of the HP filter by the series length is proposed. The examples showed the proposed method can effectively control the magnitude of fluctuation components, provides a way for the HP filter to deal with different macroeconomic time series by selecting a suitable smoothing parameter.