Boosted HP Filter: Several Properties Derived from Its Spectral Representation

The Hodrick–Prescott (HP) filter is the most prominent smoothing/trend estimation method for macroeconomic time series such as real gross domestic product. Recently, its modification, the boosted HP (bHP) filter, has been developed, and a number of studies have been conducted on it. This paper contributes to the literature by investigating the properties of the bHP filter. For this purpose, we use the spectral decomposition of the penalty matrix of the HP filter.