The Hodrick-Prescott (HP) filter is widely used in the field of economics to estimate trends and cycles from time series data. For certain applications -- such as deriving implied trend and cycle models and obtaining filter weights -- it is desirable to express the frequency response of the HP as the spectral density of an ARMA model; in other words, to accomplish the spectral factorization of the HP filter. This paper presents an exact approach to this problem, which makes it possible to provide exact algebraic formulas for the HP filter coefficients in terms of the HP's signal-noise ratio.
[PDF] or 
denotes a file in Adobe’s Portable Document Format.
To view the file, you will need the
Adobe® Acrobat® Reader
available free from Adobe.
This symbol
indicates a link to a non-government web site. Our linking to these sites does not
constitute an endorsement of any products, services or the information found on them.
Once you link to another site you are subject to the policies of the new site.
