Potential Product, Output Gap and Uncertainty Rate Associated with Their Determination while Using the Hodrick-Prescott Filter

In various fields of macroeconomic modelling, researchers often face the problem of decomposing time series into trend component and cycle fluctuations. While there are several potentially useful methods to perform the task in question, Hodrick-Prescott (HP) fi lter seems to have remained (despite some serious criticism) the most popular approach over the past decade. In this article I propose a straightforward and easy-to-implement bootstrap procedure for building pointwise and simultaneous confidence intervals around "point estimates" produced by HP filter. The principle of proposed method can be described as follows: first, we use maximum entropy bootstrap (Vinod, 2004, 2006) to approximate ensemble from which original time series is drawn and then apply the HP filter directly to each bootstrap replication. If necessary, the proposed method can be adapted to allow for uncertainty in the smoothing parameter. Practical usefulness of our approach is demonstrated with an application to the GDP data. Results are encouraging - obtained confi dence intervals for the trend and cyclical component are overall plausible thus supplying a researcher with some measure of uncertainty related to HP filtering. Finally, we demonstrate that a former approach to build confidence intervals for HP filter (Gallego and Johnson, 2005) leads to erratic inference for cycle due to the shape-destroying block bootstrap sampling.

Keywords: output gap, r, Hodrick-Prescott filter, confidence intervals, bootstrap, potential product