Estimation of the business cycle: A modified Hodrick-Prescott filter

Regina Kaiser () and Agustin Maravall ()
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Regina Kaiser: Departamento de Estadística y Econometría, Universidad Carlos III de Madrid, calle Madrid 126, E-28903 Getafe , Spain Servicio de Estudios - Banco de Espa na, Alcalá 50, E-28014 Madrid, Spain

Spanish Economic Review, 1999, vol. 1, issue 2, 175-206

Abstract: Hodrick-Prescott (HP) filtering of (most often, seasonally adjusted) quarterly series is analysed. Some of the criticism to the filter are adressed. It is seen that, while filtering strongly affects autocorrelations, it has little effect on crosscorrelations. It is argued that the criticism that HP filtering induces a spurious cycle in the series is unwarranted. The filter, however, presents two serious drawbacks: First, poor performance at the end periods, due to the size of the revisions in preliminary estimators, and, second, the amount of noise in the cyclical signal, which seriously disturbs its interpretation. We show how the addition of two model-based features (in particular, applying the filter to the series extended with proper ARIMA forecasts and backcasts, and using as input to the filter the trend-cycle component instead of the seasonally adjusted series) can considerably improve the filter performance. Throughout the discussion, we use a computationally and analytically convenient alternative derivation of the HP filter, and illustrate the results with an example consisting of 4 Spanish economic indicators.

Keywords: Time series; optimal filtering; trends; seasonality; economic cycles (search for similar items in EconPapers)
JEL-codes: C13 C22 E32 (search for similar items in EconPapers)
Date: 1999-08-06
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Working Paper: Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter (1999)
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