Exact Formulas for the Hodrick-Prescott Filter
Tucker McElroy
KEY WORDS:
ABSTRACT
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.
CITATION:
