<p>The paper reconsiders the Hodrick-Prescott filter and the issue of a suitable choice of its smoothing parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> </InlineEquation> for quarterly data. Stochastic processes generate artificial data with a known growth trend and cyclical component, and a battery of Monte Carlo experiments tests what values of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> </InlineEquation> yield the best approximation of the true trend. Specifically, the main summary statistics of the first differences are required to closely match those of the real gross value added in the US, while the average length of their cyclical fluctuations is largely compatible with the spectrograms of other business cycle data. Regarding the trend component, we distinguish between a deterministic and a stochastic trend. We find that appropriate values of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> </InlineEquation> are seven to twelve times higher than the conventional <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\lambda = 1600\)</EquationSource> </InlineEquation>. To make it more intuitive, the paper further proposes a slight modification of the filter that yields a segmented linear trend. Finally, we provide suitable values for its tuning parameter that determines the endogenous break points.</p>

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A Data-Driven Method to Determine the Smoothing Parameter in the Hodrick-Prescott Filter

  • Reiner Franke,
  • Jiri Kukacka,
  • Stephen Sacht

摘要

The paper reconsiders the Hodrick-Prescott filter and the issue of a suitable choice of its smoothing parameter \(\lambda \) for quarterly data. Stochastic processes generate artificial data with a known growth trend and cyclical component, and a battery of Monte Carlo experiments tests what values of \(\lambda \) yield the best approximation of the true trend. Specifically, the main summary statistics of the first differences are required to closely match those of the real gross value added in the US, while the average length of their cyclical fluctuations is largely compatible with the spectrograms of other business cycle data. Regarding the trend component, we distinguish between a deterministic and a stochastic trend. We find that appropriate values of \(\lambda \) are seven to twelve times higher than the conventional \(\lambda = 1600\) . To make it more intuitive, the paper further proposes a slight modification of the filter that yields a segmented linear trend. Finally, we provide suitable values for its tuning parameter that determines the endogenous break points.