Peter C. B. Phillips, Zhentao Shi
arXiv 1 May 2019 · Econometrics · publishedInternational Economic Review (2020) · 112 citations (OpenAlex)
arXiv:1905.00175 · PDF · DOI · OpenAlex · Extracted main text
The Hodrick-Prescott (HP) filter is one of the most widely used econometric methods in applied macroeconomic research. Like all nonparametric methods, the HP filter depends critically on a tuning parameter that controls the degree of smoothing. Yet in contrast to modern nonparametric methods and applied work with these procedures, empirical practice with the HP filter almost universally relies on standard settings for the tuning parameter that have been suggested largely by experimentation with macroeconomic data and heuristic reasoning. As recent research (Phillips and Jin, 2015) has shown, standard settings may not be adequate in removing trends, particularly stochastic trends, in economic data. This paper proposes an easy-to-implement practical procedure of iterating the HP smoother that is intended to make the filter a smarter smoothing device for trend estimation and trend elimination. We call this iterated HP technique the boosted HP filter in view of its connection to $L_{2}$-boosting in machine learning. The paper develops limit theory to show that the boosted HP (bHP) filter asymptotically recovers trend mechanisms that involve unit root processes, deterministic polynomial drifts, and polynomial drifts with structural breaks. A stopping criterion is used to automate the iterative HP algorithm, making it a data-determined method that is ready for modern data-rich environments in economic research. The methodology is illustrated using three real data examples that highlight the differences between simple HP filtering, the data-determined boosted filter, and an alternative autoregressive approach. These examples show that the bHP filter is helpful in analyzing a large collection of heterogeneous macroeconomic time series that manifest various degrees of persistence, trend behavior, and volatility.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hamilton, J. D., Why You Should Never Use the Hodrick-Prescott Filte… (2018) 831–843 | 1.000 | 13 | 5 | 100% |
| 2 | Aguiar, M. and G. Gopinath, Emerging Market Business Cycles: The Cyc… (2007) 69–102 | 0.874 | 6 | 2 | 100% |
| 3 | Ball, L., D. Leigh and P. Loungani, Okun's Law: Fit at 50?, Journal… (2017) 1413–1441 | 0.874 | 6 | 2 | 100% |
| 4 | Bühlmann, P. and B. Yu, Boosting with the L2 Loss: Regression and Cl… (2003) 324–339 | 0.811 | 4 | 2 | 100% |
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| 6 | Christiano, L. J. and T. J. Fitzgerald, The Band Pass Filter, Intern… (2003) 435–465 | 0.737 | 3 | 2 | 100% |
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| 8 | Hodrick, R. J. and E. C. Prescott, Postwar US Business Cycles: An Em… (1997) 1–16 | 0.737 | 3 | 2 | 100% |
| 9 | Phillips, P. C. B., Understanding Spurious Regressions in Econometri… (1998) 1299–1325 self | 0.737 | 3 | 2 | 100% |
| 10 | Corbae, D. and S. Ouliaris, Extracting Cycles from Nonstationary Dat… (2006) 167–77 | 0.644 | 2 | 2 | 100% |
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