IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2209.09810.html
   My bibliography  Save this paper

The boosted HP filter is more general than you might think

Author

Listed:
  • Ziwei Mei
  • Peter C. B. Phillips
  • Zhentao Shi

Abstract

The global financial crisis and Covid recession have renewed discussion concerning trend-cycle discovery in macroeconomic data, and boosting has recently upgraded the popular HP filter to a modern machine learning device suited to data-rich and rapid computational environments. This paper sheds light on its versatility in trend-cycle determination, explaining in a simple manner both HP filter smoothing and the consistency delivered by boosting for general trend detection. Applied to a universe of time series in FRED databases, boosting outperforms other methods in timely capturing downturns at crises and recoveries that follow. With its wide applicability the boosted HP filter is a useful automated machine learning addition to the macroeconometric toolkit.

Suggested Citation

  • Ziwei Mei & Peter C. B. Phillips & Zhentao Shi, 2022. "The boosted HP filter is more general than you might think," Papers 2209.09810, arXiv.org.
  • Handle: RePEc:arx:papers:2209.09810
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2209.09810
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Carmen M. Reinhart & Kenneth S. Rogoff, 2009. "Varieties of Crises and Their Dates," Introductory Chapters, in: This Time Is Different: Eight Centuries of Financial Folly, Princeton University Press.
    2. Liangjun Su & Zhentao Shi & Peter C. B. Phillips, 2016. "Identifying Latent Structures in Panel Data," Econometrica, Econometric Society, vol. 84, pages 2215-2264, November.
    3. Dalla, Violetta & Giraitis, Liudas & Phillips, Peter C. B., 2022. "Robust Tests For White Noise And Cross-Correlation," Econometric Theory, Cambridge University Press, vol. 38(5), pages 913-941, October.
    4. Max H. Farrell & Tengyuan Liang & Sanjog Misra, 2021. "Deep Neural Networks for Estimation and Inference," Econometrica, Econometric Society, vol. 89(1), pages 181-213, January.
    5. Phillips, Peter C.B., 2005. "Automated Discovery In Econometrics," Econometric Theory, Cambridge University Press, vol. 21(1), pages 3-20, February.
    6. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    7. Ricardo Masini & Marcelo C. Medeiros, 2021. "Counterfactual Analysis With Artificial Controls: Inference, High Dimensions, and Nonstationarity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1773-1788, October.
    8. Andrii Babii & Eric Ghysels & Jonas Striaukas, 2022. "Machine Learning Time Series Regressions With an Application to Nowcasting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1094-1106, June.
    9. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    10. Johansen, Søren, 1995. "A Stastistical Analysis of Cointegration for I(2) Variables," Econometric Theory, Cambridge University Press, vol. 11(1), pages 25-59, February.
    11. Caner, Mehmet & Kock, Anders Bredahl, 2018. "Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso," Journal of Econometrics, Elsevier, vol. 203(1), pages 143-168.
    12. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2021. "Matrix Completion Methods for Causal Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1716-1730, October.
    13. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    14. James D. Hamilton, 2018. "Why You Should Never Use the Hodrick-Prescott Filter," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 831-843, December.
    15. Kristian Jönsson, 2020. "Cyclical Dynamics and Trend/Cycle Definitions: Comparing the HP and Hamilton Filters," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 16(2), pages 151-162, November.
    16. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    17. Michael W. McCracken & Serena Ng, 2021. "FRED-QD: A Quarterly Database for Macroeconomic Research," Review, Federal Reserve Bank of St. Louis, vol. 103(1), pages 1-44, January.
    18. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
    19. Lee, Sokbae & Liao, Yuan & Seo, Myung Hwan & Shin, Youngki, 2021. "Sparse HP filter: Finding kinks in the COVID-19 contact rate," Journal of Econometrics, Elsevier, vol. 220(1), pages 158-180.
    20. Buhlmann P. & Yu B., 2003. "Boosting With the L2 Loss: Regression and Classification," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 324-339, January.
    21. Andrii Babii & Eric Ghysels & Jonas Striaukas, 2022. "Machine Learning Time Series Regressions With an Application to Nowcasting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1094-1106, June.
    22. Adriana Cornea-Madeira, 2017. "The Explicit Formula for the Hodrick-Prescott Filter in a Finite Sample," The Review of Economics and Statistics, MIT Press, vol. 99(2), pages 314-318, May.
    23. Viv B. Hall & Peter Thomson, 2021. "Does Hamilton’s OLS Regression Provide a “better alternative” to the Hodrick-Prescott Filter? A New Zealand Business Cycle Perspective," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 17(2), pages 151-183, November.
    24. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    25. Yamada, Hiroshi, 2020. "A Smoothing Method That Looks Like The Hodrick–Prescott Filter," Econometric Theory, Cambridge University Press, vol. 36(5), pages 961-981, October.
    26. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    27. Robert M. de Jong & Neslihan Sakarya, 2016. "The Econometrics of the Hodrick-Prescott Filter," The Review of Economics and Statistics, MIT Press, vol. 98(2), pages 310-317, May.
    28. Niels Haldrup, 1998. "An Econometric Analysis of I(2) Variables," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 595-650, December.
    29. Sakarya, Neslihan & de Jong, Robert M., 2020. "A Property Of The Hodrick–Prescott Filter And Its Application," Econometric Theory, Cambridge University Press, vol. 36(5), pages 840-870, October.
    30. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    31. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    32. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2014. "Inference on Treatment Effects after Selection among High-Dimensional Controlsâ€," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 608-650.
    33. Jushan Bai & Serena Ng, 2009. "Boosting diffusion indices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 607-629.
    34. Phillips, Peter C.B., 2023. "Estimation And Inference With Near Unit Roots," Econometric Theory, Cambridge University Press, vol. 39(2), pages 221-263, April.
    35. Josefine Quast & Maik H. Wolters, 2022. "Reliable Real-Time Output Gap Estimates Based on a Modified Hamilton Filter," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 152-168, January.
    36. Niels Haldrup, 1998. "An Econometric Analysis of I(2) Variables," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 595-650, December.
    37. Cogley, Timothy & Nason, James M., 1995. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 253-278.
    38. Morten O. Ravn & Harald Uhlig, 2002. "On adjusting the Hodrick-Prescott filter for the frequency of observations," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 371-375.
    39. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    40. Yamada, Hiroshi, 2022. "Trend Extraction From Economic Time Series With Missing Observations By Generalized Hodrick–Prescott Filters," Econometric Theory, Cambridge University Press, vol. 38(3), pages 419-453, June.
    41. Mathias Drehmann & James Yetman, 2018. "Why you should use the Hodrick-Prescott filter - at least to generate credit gaps," BIS Working Papers 744, Bank for International Settlements.
    42. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ziwei Mei & Zhentao Shi, 2022. "On LASSO for High Dimensional Predictive Regression," Papers 2212.07052, arXiv.org, revised Jan 2024.
    2. Andrii Babii & Eric Ghysels & Jonas Striaukas, 2023. "Econometrics of Machine Learning Methods in Economic Forecasting," Papers 2308.10993, arXiv.org.
    3. Ye Lu & Adrian Pagan, 2023. "To Boost or Not to Boost? That is the Question," CAMA Working Papers 2023-12, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    4. Eva Biswas & Farzad Sabzikar & Peter C. B. Phillips, 2022. "Boosting the HP Filter for Trending Time Series with Long Range Dependence," Cowles Foundation Discussion Papers 2347, Cowles Foundation for Research in Economics, Yale University.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peter C. B. Phillips & Zhentao Shi, 2021. "Boosting: Why You Can Use The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 521-570, May.
    2. Peter C. B. Phillips & Sainan Jin, 2021. "Business Cycles, Trend Elimination, And The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 469-520, May.
    3. Peter C.B. Phillips & Zhentao Shi, 2019. "Boosting the Hodrick-Prescott Filter," Cowles Foundation Discussion Papers 2192, Cowles Foundation for Research in Economics, Yale University.
    4. Ziwei Mei & Zhentao Shi, 2022. "On LASSO for High Dimensional Predictive Regression," Papers 2212.07052, arXiv.org, revised Jan 2024.
    5. Viv B. Hall & Peter Thomson, 2021. "Does Hamilton’s OLS Regression Provide a “better alternative” to the Hodrick-Prescott Filter? A New Zealand Business Cycle Perspective," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 17(2), pages 151-183, November.
    6. Melina Dritsaki & Chaido Dritsaki, 2022. "Comparison of HP Filter and the Hamilton’s Regression," Mathematics, MDPI, vol. 10(8), pages 1-18, April.
    7. Neslihan Sakarya & Robert M. de Jong, 2022. "The spectral analysis of the Hodrick–Prescott filter," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 479-489, May.
    8. Anindya Banerjee & Paul Mizen, 2006. "A re‐interpretation of the linear quadratic model when inventories and sales are polynomially cointegrated," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1249-1264, December.
    9. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    10. Ugo Panizza, 2022. "Do Countries Default in Bad Times? The Role of Alternative Detrending Techniques," IHEID Working Papers 06-2022, Economics Section, The Graduate Institute of International Studies.
    11. Carnazza, Giovanni & Liberati, Paolo & Sacchi, Agnese, 2020. "The cyclically-adjusted primary balance: A novel approach for the euro area," Journal of Policy Modeling, Elsevier, vol. 42(5), pages 1123-1145.
    12. Jylhä, Petri & Lof, Matthijs, 2022. "Mind the Basel gap," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 79(C).
    13. Hiroshi Yamada, 2023. "Quantile regression version of Hodrick–Prescott filter," Empirical Economics, Springer, vol. 64(4), pages 1631-1645, April.
    14. Hall, Viv B & Thomson, Peter, 2022. "A boosted HP filter for business cycle analysis: evidence from New Zealand’s small open economy," Working Paper Series 9473, Victoria University of Wellington, School of Economics and Finance.
    15. Hartwig, Benny & Meinerding, Christoph & Schüler, Yves S., 2021. "Identifying indicators of systemic risk," Journal of International Economics, Elsevier, vol. 132(C).
    16. Peter C.B. Phillips, 2001. "Bootstrapping Spurious Regression," Cowles Foundation Discussion Papers 1330, Cowles Foundation for Research in Economics, Yale University.
    17. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    18. Arranz, Miguel A. & Escribano, Álvaro & Mármol, Francesc, 2002. "Effects of Applying Linear and Nonlinear Filters on Tests for Unit Roots with Additive Outliers," UC3M Working papers. Economics we20091101, Universidad Carlos III de Madrid. Departamento de Economía.
    19. Wolf, Elias & Mokinski, Frieder & Schüler, Yves, 2020. "On adjusting the one-sided Hodrick-Prescott filter," Discussion Papers 11/2020, Deutsche Bundesbank.
    20. Lin, Yingqian & Tu, Yundong, 2020. "Robust inference for spurious regressions and cointegrations involving processes moderately deviated from a unit root," Journal of Econometrics, Elsevier, vol. 219(1), pages 52-65.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2209.09810. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.