IDEAS home Printed from
   My bibliography  Save this paper

Real Time Estimation in Local Polynomial Regression, with Application to Trend-Cycle Analysis




The paper focuses on the adaptation of local polynomial filters at the end of the sample period. We show that for real time estimation of signals (i.e. exactly at the boundary of the time support) we cannot rely on the automatic adaptation of the local polynomial smoothers, since the direct real time filter turns out to be strongly localised, and thereby yields extremely volatile estimates. As an alternative we evaluate a general family of asymmetric filters that minimises the mean square revision error subject to polynomial reproduction constraints; in the case of the Henderson filter it nests the well known Musgrave’s surrogate filters. The class of filters depends on unknown features of the series such as the slope and the curvature of the underlying signal, which can be estimated from the data. Several empirical examples illustrate the effectiveness of our proposal. We also discuss the merits of using a nearest neighbour bandwidth as opposed to a fixed bandwidth for improving the quality of the approximation.

Suggested Citation

  • Tommaso Proietti & Alessandra Luati, 2008. "Real Time Estimation in Local Polynomial Regression, with Application to Trend-Cycle Analysis," CEIS Research Paper 112, Tor Vergata University, CEIS, revised 14 Jul 2008.
  • Handle: RePEc:rtv:ceisrp:112

    Download full text from publisher

    File URL:
    File Function: Main text
    Download Restriction: no

    References listed on IDEAS

    1. Edward E. Leamer, 2007. "Housing is the business cycle," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 149-233.
    2. Quenneville, Benoit & Ladiray, Dominique & Lefrancois, Bernard, 2003. "A note on Musgrave asymmetrical trend-cycle filters," International Journal of Forecasting, Elsevier, vol. 19(4), pages 727-734.
    3. Estela Bee Dagum & Alessandra Luati, 2009. "A Cascade Linear Filter to Reduce Revisions and False Turning Points for Real Time Trend-Cycle Estimation," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 40-59.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, February.
    5. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, February.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Marlon Fritz & Thomas Gries & Yuanhua Feng, 2019. "Growth Trends and Systematic Patterns of Booms and Busts‐Testing 200 Years of Business Cycle Dynamics," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(1), pages 62-78, February.
    2. Yuanhua Feng & Thomas Gries, 2017. "Data-driven local polynomial for the trend and its derivatives in economic time series," Working Papers CIE 102, Paderborn University, CIE Center for International Economics.
    3. Proietti, Tommaso & Luati, Alessandra, 2009. "Low-Pass Filter Design using Locally Weighted Polynomial Regression and Discrete Prolate Spheroidal Sequences," MPRA Paper 15510, University Library of Munich, Germany.
    4. Bianconcini, Silvia & Quenneville, Benoit, 2010. "Real Time Analysis Based on Reproducing Kernel Henderson Filters/Análisis en tiempo real basado en la reproducción de los filtros de núcleo de Henderson," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 28, pages 553-574, Diciembre.
    5. 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.
    6. Michel Grun-Rehomme & OLGA VASYECHKO, 2013. "Methodes De Lissage D’Une Serie Temporelle :Le Probleme Des Extremites," Brussels Economic Review, ULB -- Universite Libre de Bruxelles, vol. 56(2), pages 163-174.

    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. Blöchl, Andreas, 2014. "Penalized Splines as Frequency Selective Filters - Reducing the Excess Variability at the Margins," Discussion Papers in Economics 20687, University of Munich, Department of Economics.
    2. Bloechl, Andreas, 2014. "Penalized Splines, Mixed Models and the Wiener-Kolmogorov Filter," Discussion Papers in Economics 21406, University of Munich, Department of Economics.
    3. Zanin, Luca & Marra, Giampiero, 2012. "Assessing the functional relationship between CO2 emissions and economic development using an additive mixed model approach," Economic Modelling, Elsevier, vol. 29(4), pages 1328-1337.
    4. Ni, Xiao & Zhang, Hao Helen & Zhang, Daowen, 2009. "Automatic model selection for partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2100-2111, October.
    5. Proietti, Tommaso, 2010. "Trend Estimation," MPRA Paper 21607, University Library of Munich, Germany.
    6. Otto-Sobotka, Fabian & Salvati, Nicola & Ranalli, Maria Giovanna & Kneib, Thomas, 2019. "Adaptive semiparametric M-quantile regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 116-129.
    7. Javier Parada Gómez Urquiza & Alejandro López-Feldman, 2013. "Poverty dynamics in rural Mexico: What does the future hold?," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 55-74, November.
    8. Bethany Everett & David Rehkopf & Richard Rogers, 2013. "The Nonlinear Relationship Between Education and Mortality: An Examination of Cohort, Race/Ethnic, and Gender Differences," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 32(6), pages 893-917, December.
    9. Tatiyana V. Apanasovich & David Ruppert & Joanne R. Lupton & Natasa Popovic & Nancy D. Turner & Robert S. Chapkin & Raymond J. Carroll, 2008. "Aberrant Crypt Foci and Semiparametric Modeling of Correlated Binary Data," Biometrics, The International Biometric Society, vol. 64(2), pages 490-500, June.
    10. Eduardo L. Montoya & Wendy Meiring, 2016. "An F-type test for detecting departure from monotonicity in a functional linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 322-337, June.
    11. Yu, Jun, 2012. "A semiparametric stochastic volatility model," Journal of Econometrics, Elsevier, vol. 167(2), pages 473-482.
    12. Timothy K.M. Beatty & Erling Røed Larsen, 2005. "Using Engel curves to estimate bias in the Canadian CPI as a cost of living index," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 38(2), pages 482-499, May.
    13. Mestekemper, Thomas & Windmann, Michael & Kauermann, Göran, 2010. "Functional hourly forecasting of water temperature," International Journal of Forecasting, Elsevier, vol. 26(4), pages 684-699, October.
    14. Naschold, Felix, 2012. "“The Poor Stay Poor”: Household Asset Poverty Traps in Rural Semi-Arid India," World Development, Elsevier, vol. 40(10), pages 2033-2043.
    15. Arthur Charpentier & Emmanuel Flachaire & Antoine Ly, 2017. "Econom\'etrie et Machine Learning," Papers 1708.06992,, revised Mar 2018.
    16. Jaroslaw Harezlak & Louise M. Ryan & Jay N. Giedd & Nicholas Lange, 2005. "Individual and Population Penalized Regression Splines for Accelerated Longitudinal Designs," Biometrics, The International Biometric Society, vol. 61(4), pages 1037-1048, December.
    17. Hyunju Son & Youyi Fong, 2021. "Fast grid search and bootstrap‐based inference for continuous two‐phase polynomial regression models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    18. Welham, S.J. & Thompson, R., 2009. "A note on bimodality in the log-likelihood function for penalized spline mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 920-931, February.
    19. Michael Wegener & Göran Kauermann, 2017. "Forecasting in nonlinear univariate time series using penalized splines," Statistical Papers, Springer, vol. 58(3), pages 557-576, September.
    20. Dlugosz, Stephan & Mammen, Enno & Wilke, Ralf A., 2017. "Generalized partially linear regression with misclassified data and an application to labour market transitions," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 145-159.

    More about this item


    Henderson filter. Trend estimation. Nearest Neighbour Bandwidth. Musgrave asymmetric filters;

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:rtv:ceisrp:112. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: .

    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: Barbara Piazzi (email available below). General contact details of provider: .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.