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Exact formulas for the Hodrick-Prescott filter

Author

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  • Tucker McElroy

Abstract

The Hodrick--Prescott (HP) filter is widely used in the field of economics to estimate trends and cycles from time series data. For certain applications--such as deriving implied trend and cycle models and obtaining filter weights--it is desirable to express the frequency response of the HP as the spectral density of an ARMA model; in other words, to accomplish the spectral factorization of the HP filter. This paper presents an exact approach to this problem, which makes it possible to provide exact algebraic formulas for the HP filter coefficients in terms of the HP's signal-to-noise ratio. Copyright Royal Economic Society 2008

Suggested Citation

  • Tucker McElroy, 2008. "Exact formulas for the Hodrick-Prescott filter," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 209-217, March.
    • Handle: RePEc:ect:emjrnl:v:11:y:2008:i:1:p:209-217
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    Citations

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    Cited by:

    1. Coeurdacier, Nicolas & Kollmann, Robert & Martin, Philippe, 2010. "International portfolios, capital accumulation and foreign assets dynamics," Journal of International Economics, Elsevier, vol. 80(1), pages 100-112, January.
    2. Henry R. Hyatt & Tucker S. McElroy, 2019. "Labor Reallocation, Employment, and Earnings: Vector Autoregression Evidence," LABOUR, CEIS, vol. 33(4), pages 463-487, December.
    3. Maravall, A. & del Rio, A., 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 975-998, October.
    4. 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.
    5. James D. Hamilton, 2017. "Why You Should Never Use the Hodrick-Prescott Filter," NBER Working Papers 23429, National Bureau of Economic Research, Inc.
    6. Coeurdacier, Nicolas & Kollmann, Robert & Martin, Philippe, 2010. "International portfolios, capital accumulation and foreign assets dynamics," Journal of International Economics, Elsevier, vol. 80(1), pages 100-112, January.
    7. Viv B Hall & Peter Thomson, 2020. "Does Hamilton’s OLS regression provide a “better alternative†to the Hodrick-Prescott filter? A New Zealand business cycle perspective," CAMA Working Papers 2020-71, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    8. 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.
    9. Dilip Nachane & Aditi Chaubal, 2022. "A Comparative Evaluation of Some DSP Filters vis-à-vis Commonly Used Economic Filters," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 161-190, September.
    10. Viv B. Hall & Peter Thomson, 2022. "A boosted HP filter for business cycle analysis:evidence from New Zealand's small open economy," CAMA Working Papers 2022-45, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    11. repec:hal:spmain:info:hdl:2441/c8dmi8nm4pdjkuc9g7084aa4m is not listed on IDEAS
    12. McElroy, Tucker S. & Wildi, Marc, 2020. "The Multivariate Linear Prediction Problem: Model-Based and Direct Filtering Solutions," Econometrics and Statistics, Elsevier, vol. 14(C), pages 112-130.
    13. Elżbieta Szaruga & Zuzanna Kłos-Adamkiewicz & Agnieszka Gozdek & Elżbieta Załoga, 2021. "Linkages between Energy Delivery and Economic Growth from the Point of View of Sustainable Development and Seaports," Energies, MDPI, vol. 14(14), pages 1-61, July.
    14. Henry R. Hyatt & Tucker S. McElroy, 2017. "Labor Reallocation, Employment, and Earnings: Vector Autoregression Evidence," Working Papers 17-11r, Center for Economic Studies, U.S. Census Bureau.
    15. 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.
    16. repec:hal:wpspec:info:hdl:2441/c8dmi8nm4pdjkuc9g7084aa4m is not listed on IDEAS
    17. Wildi Marc & McElroy Tucker, 2016. "Optimal Real-Time Filters for Linear Prediction Problems," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 155-192, July.
    18. Kiki Verico, 2021. "Global Pandemic 2020: Indonesia’s Output Gap and Middle-Income Trap Scenario," LPEM FEBUI Working Papers 202157, LPEM, Faculty of Economics and Business, University of Indonesia, revised 2021.
    19. McElroy, Tucker & Wildi, Marc, 2013. "Multi-step-ahead estimation of time series models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 378-394.
    20. 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.
    21. Nicolas Coeurdacier, 2011. "Limited participation and International Risk-Sharing," 2011 Meeting Papers 613, Society for Economic Dynamics.
    22. Kristian Jönsson, 2010. "Trend extraction with a judgement-augmented hodrick–prescott filter," Empirical Economics, Springer, vol. 39(3), pages 703-711, December.
    23. repec:spo:wpecon:info:hdl:2441/c8dmi8nm4pdjkuc9g7084aa4m is not listed on IDEAS

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