Macroeconomic model reference

HP filter and Beveridge-Nelson decomposition Model

Trend-cycle decomposition for a single macro series, comparing smooth HP trend extraction with Beveridge-Nelson permanent-transitory decomposition.

Empirical forecasting models · Sources

HP filter and Beveridge-Nelson decomposition sources, papers, and evidence trail

Primary papers, model variants, source notes, and review signals behind the HP filter and Beveridge-Nelson decomposition page.

Staff papers, NBER-style drafts, and research notes used where the live literature has not fully settled.

[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

Reference material used for orientation; read primary and academic sources first when claims conflict.

[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.
Reference
[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.
Reference
[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.
Reference
[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.
Reference
[S6] Reference
Ravn and Uhlig (2002) derived frequency-consistent lambda values across data frequencies: lambda = 6.25 (annual), 1600 (quarterly), 129600 (monthly).
Reference
[S7] Reference
Cogley and Nason (1995) showed that the HP filter can generate spurious business-cycle periodicity when applied to difference-stationary data.
Reference

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Data-Driven Models

References

Staff papers, NBER-style drafts, and research notes used where the live literature has not fully settled.

[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

Reference material used for orientation; read primary and academic sources first when claims conflict.

[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.
Reference
[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.
Reference
[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.
Reference
[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.
Reference
[S6] Reference
Ravn and Uhlig (2002) derived frequency-consistent lambda values across data frequencies: lambda = 6.25 (annual), 1600 (quarterly), 129600 (monthly).
Reference
[S7] Reference
Cogley and Nason (1995) showed that the HP filter can generate spurious business-cycle periodicity when applied to difference-stationary data.
Reference