Discussion Papers,
Statistics Norway, Research Department

Abstract: This paper introduces two methodological improvements to the Hodrick– Prescott (HP) filter for decomposing GDP into trend and cycle components. First, we propose a robust univariate filter that accounts for extreme observations — such as the COVID–19 pandemic — by treating them as additive outliers. Second, we develop a multivariate HP filter that incorporates time–varying, import– adjusted budget shares of GDP sub–components. This adaptive weighting minimizes cyclical variance and yields a more stable trend estimate. Applying the framework to U.S. data, we find that private investment is the dominant source of cyclical fluctuations, while government expenditure exhibits a persistent counter–cyclical pattern. The proposed approach enhances real–time policy analysis by reducing endpoint bias and improving the identification of cyclical dynamics.

Keywords: output gap; Hodrick–Prescott filter; robust filtering; multivariate decomposition; additive outliers; time–varying budget shares; business cycle analysis

JEL-codes: E32; C22; E37; C43; C51

40 pages, December 2025

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