IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v76y2008i2p187-202.html
   My bibliography  Save this article

Estimating Trends with Percentage of Smoothness Chosen by the User

Author

Listed:
  • Victor M. Guerrero

Abstract

This work presents a method for estimating trends of economic time series that allows the user to fix at the outset the desired percentage of smoothness for the trend. The calculations are based on the Hodrick‐Prescott (HP) filter usually employed in business cycle analysis. The situation considered here is not related to that kind of analysis, but with describing the dynamic behaviour of the series by way of a smooth curve. To apply the filter, the user has to specify a smoothing constant that determines the dynamic behaviour of the trend. A new method that formalizes the concept of trend smoothness is proposed here to choose that constant. Smoothness of the trend is measured in percentage terms with the aid of an index related to the underlying statistical model of the HP filter. Empirical illustrations are provided using data on Mexico's GDP. Ce travail présente un méthode pour estimer les tendances des séries de temps économiques qui permet à l'usager fixer dès début le pourcentage désiré de douceur pour la tendance. Les calculs ont fondement en le filtre de Hodrick et Prescott que s'emploie généralement dans l'analyse de cycles économiques. La situation ici considéré n'a pas relation avec ce type d'analyse, mais comment la description du comportement dynamique des séries avec une courbe douce. Pour appliquer le filtre, l'usager a besoin de spécifier une constante de douceur que détermine le comportement dynamique de la tendance. Un nouveau méthode que formalise le concept de douceur de la tendance est ici proposé pour choisir la constante. La douceur de la tendance est mesuré en termes de pourcentage avec l'aide d'un index rapporté avec le modèle statistique après le filtre. Quelques illustrations empiriques sont munies avec données de l'économie mexicaine.

Suggested Citation

  • Victor M. Guerrero, 2008. "Estimating Trends with Percentage of Smoothness Chosen by the User," International Statistical Review, International Statistical Institute, vol. 76(2), pages 187-202, August.
    • Handle: RePEc:bla:istatr:v:76:y:2008:i:2:p:187-202
    DOI: 10.1111/j.1751-5823.2008.00047.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1751-5823.2008.00047.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1751-5823.2008.00047.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    2. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-751, May.
    3. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
    4. Kaiser, Regina & Maravall, Agustin, 2005. "Combining filter design with model-based filtering (with an application to business-cycle estimation)," International Journal of Forecasting, Elsevier, vol. 21(4), pages 691-710.
    5. Maravall, Agustin, 1993. "Stochastic linear trends : Models and estimators," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 5-37, March.
    6. Peter Young, 1999. "Recursive and en-bloc approaches to signal extraction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(1), pages 103-128.
    7. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-247, July-Sept.
    8. Lee, Thomas C. M., 2003. "Smoothing parameter selection for smoothing splines: a simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 139-148, February.
    9. Pedersen, Torben Mark, 2001. "The Hodrick-Prescott filter, the Slutzky effect, and the distortionary effect of filters," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1081-1101, August.
    10. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    11. 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.
    12. 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.
    13. Guerrero, Víctor M. & Juárez, Rodrigo & Poncela, Pilar, 2001. "Data graduation based on statistical time series methods," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 169-175, April.
    14. 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.
    15. Park, Gonyung, 1996. "The role of detrending methods in a model of real business cycles," Journal of Macroeconomics, Elsevier, vol. 18(3), pages 479-501.
    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. A. ISLAS & Víctor M. GUERRERO & Eliud SILVA, 2019. "Forecasting Remittances to Mexico with a Multi-State Markov-Switching Model Applied to the Trend with Controlled Smoothness," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 38-56, March.
    2. Víctor M. Guerrero & Adriana Galicia‐Vázquez, 2010. "Trend estimation of financial time series," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 205-223, May.
    3. Eliud Silva & Víctor M. Guerrero, 2017. "Penalized least squares smoothing of two-dimensional mortality tables with imposed smoothness," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1662-1679, July.
    4. Víctor M. Guerrero & Daniela Cortés Toto & Hortensia J. Reyes Cervantes, 2018. "Effect of autocorrelation when estimating the trend of a time series via penalized least squares with controlled smoothness," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 109-130, March.

    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. Mark Meyer & Peter Winker*, 2005. "Using HP Filtered Data for Econometric Analysis: Some Evidence from Monte Carlo Simulations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 89(3), pages 303-320, August.
    2. Lars-H. R. Siemers, 2024. "On the Hamilton-HP Filter Controversy: Evidence from German Business Cycles," MAGKS Papers on Economics 202421, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    3. Melina Dritsaki & Chaido Dritsaki, 2022. "Comparison of HP Filter and the Hamilton’s Regression," Mathematics, MDPI, vol. 10(8), pages 1-18, April.
    4. Robert J. Hodrick, 2020. "An Exploration of Trend-Cycle Decomposition Methodologies in Simulated Data," NBER Working Papers 26750, National Bureau of Economic Research, Inc.
    5. Alain Guay & Pierre Saint-Amant, 2005. "Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?," Annals of Economics and Statistics, GENES, issue 77, pages 133-155.
    6. Álvarez, Luis J. & Gómez-Loscos, Ana, 2018. "A menu on output gap estimation methods," Journal of Policy Modeling, Elsevier, vol. 40(4), pages 827-850.
    7. Kozicki, Sharon, 1999. "Multivariate detrending under common trend restrictions: Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 23(7), pages 997-1028, June.
    8. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    9. Tawadros, George B., 2011. "The stylised facts of Australia's business cycle," Economic Modelling, Elsevier, vol. 28(1), pages 549-556.
    10. Alain Guay & Pierre St-Amant, 1996. "Do Mechanical Filters Provide a Good Approximation of Business Cycles?," Technical Reports 78, Bank of Canada.
    11. Ard den Reijer, 2006. "The Dutch business cycle: which indicators should we monitor?," DNB Working Papers 100, Netherlands Central Bank, Research Department.
    12. Galimberti, Jaqueson K. & Moura, Marcelo L., 2016. "Improving the reliability of real-time output gap estimates using survey forecasts," International Journal of Forecasting, Elsevier, vol. 32(2), pages 358-373.
    13. 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.
    14. 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.
    15. 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.
    16. Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
    17. Günes Kamber & James Morley & Benjamin Wong, 2018. "Intuitive and Reliable Estimates of the Output Gap from a Beveridge-Nelson Filter," The Review of Economics and Statistics, MIT Press, vol. 100(3), pages 550-566, July.
    18. Massmann, Michael & Mitchell, James, 2003. "Reconsidering the evidence: Are Eurozone business cycles converging," ZEI Working Papers B 05-2003, University of Bonn, ZEI - Center for European Integration Studies.
    19. Pollock D. S. G., 2013. "Cycles, Syllogisms and Semantics: Examining the Idea of Spurious Cycles," Journal of Time Series Econometrics, De Gruyter, vol. 6(1), pages 81-102, September.
    20. Aadland, David, 2005. "Detrending time-aggregated data," Economics Letters, Elsevier, vol. 89(3), pages 287-293, December.

    More about this item

    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:bla:istatr:v:76:y:2008:i:2:p:187-202. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.html .

    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.