HP filter and Beveridge-Nelson decomposition Model

[S1] Working paper

Hodrick and Prescott (1997) defined the penalized least-squares filter with lambda = 1600 for quarterly data. The working paper circulated from 1980; the published version became the most cited detrending method in macroeconomics.

Working paper

[S2] Reference

Beveridge and Nelson (1981) proved that any I(1) process admits a unique decomposition into a random walk (permanent) and a stationary (transitory) component via the Wold representation.

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[S3] Reference

King and Rebelo (1993) derived the HP filter's frequency-response function and showed it approximates an ideal high-pass filter, connecting it to band-pass methods.

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[S4] Reference

Morley, Nelson, and Zivot (2003) demonstrated that the BN decomposition is equivalent to a correlated-components UCM, reconciling the HP and BN traditions within a single framework.

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[S5] Reference

Hamilton (2018) showed that the HP filter creates spurious dynamic relations in integrated data and proposed a regression-based alternative that avoids end-point bias.

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[S6] Reference

Ravn and Uhlig (2002) derived frequency-consistent lambda values across data frequencies: lambda = 6.25 (annual), 1600 (quarterly), 129600 (monthly).

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[S7] Reference

Cogley and Nason (1995) showed that the HP filter can generate spurious business-cycle periodicity when applied to difference-stationary data.

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