The alternative of a smoother parameter in the Hodrick-Prescott filter

From its beginnings in the second half of the nineteenth century until today, the study of economic time series has involved a variety of research anchored in stylized mathematical methods in order to simulate, verify, test, and forecast the behavior of key economic variables to describe economic activity and its phenomena intertemporally. Despite the proliferation of studies, it was not until the 1980s that the procedure outlined by Robert James Hodrick and Edward Christian Prescott acquired special relevance. Their method, isolating the effects and trend-cycle series, denoted a turning point in modern econometric modeling. However, the spread of the "HP filter" in economic applications used by researchers, academics, students, and policy-makers has led to implausible results because of inadequate specifications in the decomposition of the series. In this context, this analysis attempts to overcome the methodological problems inherent in the filter, indicate a brief theoretical outline of the time series, formulate a sui generis consistent parameter of variables, and show in Stata a simulation of the real exchange rate in Norway.