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Quantile regression version of Hodrick–Prescott filter

Author

Listed:
  • Hiroshi Yamada

    (Hiroshima University)

Abstract

Hodrick–Prescott (HP) filter is a popular trend filtering method for univariate macroeconomic time series such as real gross domestic product. This paper considers the quantile regression version of HP filter (qHP filter), which is a filtering method defined by replacing quadratic loss function of HP filter with quantile regression loss function. One of the essential properties of quantile regression is that if the regression includes intercept, then the ratio of negative residuals can be almost controlled. Does the suggested qHP filter also have the property? This paper answers this question. In addition to the main result, we provide an empirical illustration.

Suggested Citation

  • Hiroshi Yamada, 2023. "Quantile regression version of Hodrick–Prescott filter," Empirical Economics, Springer, vol. 64(4), pages 1631-1645, April.
    • Handle: RePEc:spr:empeco:v:64:y:2023:i:4:d:10.1007_s00181-022-02292-8
    DOI: 10.1007/s00181-022-02292-8
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    References listed on IDEAS

    as
    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. Hiroshi Yamada, 2018. "Several least-squares problems related to the Hodrick–Prescott filtering," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(5), pages 1022-1027, March.
    3. 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.
    4. 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.
    5. Hiroshi Yamada & Fatima Tuj Jahra, 2019. "Explicit formulas for the smoother weights of the Whittaker–Henderson graduation of order 1," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(12), pages 3153-3161, June.
    6. Ulrich K. Müller & Mark W. Watson, 2018. "Long†Run Covariability," Econometrica, Econometric Society, vol. 86(3), pages 775-804, May.
    7. Weinert, Howard L., 2007. "Efficient computation for Whittaker-Henderson smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 959-974, October.
    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. Hiroshi Yamada, 2018. "Why does the trend extracted by the Hodrick–Prescott filtering seem to be more plausible than the linear trend?," Applied Economics Letters, Taylor & Francis Journals, vol. 25(2), pages 102-105, January.
    10. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Hodrick–Prescott filter; Quantile regression; Penalized regression;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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