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Exact Formulas for the Hodrick-Prescott Filter

Tucker S. McElroy(1)

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.

KEYWORDS:

Nonstationary time series, filtering, business cycle





(1) Tucker S. McElroy is Mathematical Statistican, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : Tucker.S.McElroy@census.gov



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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or x12@census.gov) |  Last Revised: November 19, 2012