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Decomposing the Output Gap. Robust Univariate and Multivariate Hodrick–Prescott Filtering with Extreme Observations

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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.

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  • Håvard Hungnes, 2025. "Decomposing the Output Gap. Robust Univariate and Multivariate Hodrick–Prescott Filtering with Extreme Observations," Discussion Papers 1031, Statistics Norway, Research Department.
    • Handle: RePEc:ssb:dispap:1031
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    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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