Quantile regression version of Hodrick–Prescott filter

Abstract Hodrick–Prescott (HP) filter is a popular trend filtering method for univariate macroeconomic time series such as real gross domestic product. This paper considers the quantile regression version of HP (qHP filter), which defined by replacing quadratic loss function with function. One essential properties that if includes intercept, then ratio negative residuals can be almost controlled. Does suggested qHP also have property? answers this question. In addition to main result, we provide an empirical illustration.