Econometrics Seminar - Ye Lu (University of Sydney)

Title: Spectral centroid targeting with the HP filter

Abstract: The Hodrick-Prescott (HP) filter is one of the most widely used nonparametric econometric methods for trend-cycle decomposition in applied macroeconomic and financial economic research. The performance of the filter, like all nonparametric methods, depends critically on a tuning parameter that controls the degree of smoothing. Most of the empirical practice with HP filter, however, universally sets the tuning parameter (when quarterly data is used) as a single number, 1600, which was suggested originally by Hodrick and Prescott based largely on experimentation with macroeconomic data in their business cycle analysis. In this paper, we propose a cycle frequency-targeted and data-dependent approach to determine the tuning parameter in the HP filter which yields more reliable and economically meaningful trend and cycle estimates. To achieve this, we first show that the limiting processes of the HP filtered trend and cycle components can be expressed as weighted averages of sinusoids with a spectrum of frequencies, where the weights depend explicitly on the choice of tuning parameter. Next, we introduce a measure named `spectral centroid’ which can effectively characterize the center of the mass of the frequency/period of a process and derive a formula to relate the spectral centroid of the cycle component from HP filter and the functional form of tuning parameter. This formula allows us to solve for the tuning parameter from the targeted spectral centroid of the cycle component and the sample size of the data. The proposed method to determine the crucial tuning parameter is particularly useful given that in practice HP filter have been used in various types of tasks where researchers may be interested in targeting cycles with different lengths in their estimation (e.g., it is known that financial cycles are often much longer than business cycles). Lastly, we extend our analysis to the one-sided version of the HP filter which is popularly used in the real-time estimation of output gaps and credit gaps.