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

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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.

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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    Keywords

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

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