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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. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    2. 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.
    3. Gerhard Bry & Charlotte Boschan, 1971. "Cyclical Analysis of Time Series: Selected Procedures and Computer Programs," NBER Books, National Bureau of Economic Research, Inc, number bry_71-1.
    4. Edward E. Leamer, 2007. "Housing is the business cycle," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 149-233.
    5. 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.
    6. Gerhard Bry & Charlotte Boschan, 1971. "Foreword to "Cyclical Analysis of Time Series: Selected Procedures and Computer Programs"," NBER Chapters, in: Cyclical Analysis of Time Series: Selected Procedures and Computer Programs, pages -1, National Bureau of Economic Research, Inc.
    7. 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.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    9. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
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    1. 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.
    2. Saverio Ranciati & Alberto Roverato & Alessandra Luati, 2021. "Fused graphical lasso for brain networks with symmetries," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1299-1322, November.
    3. Webel, Karsten & Smyk, Anna, 2023. "Towards seasonal adjustment of infra-monthly time series with JDemetra+," Discussion Papers 24/2023, Deutsche Bundesbank.
    4. 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.
    5. 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.
    6. Tina Kalayil & Somya Tyagi & Mahfuza Khatun & Sikandar Siddiqui, 2019. "A Risk-Sensitive Momentum Approach To Stock Selection," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 64(220), pages 61-84, January –.
    7. 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.
    8. 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.
    9. Webel, Karsten, 2025. "Revisions in concurrent seasonal adjustments of daily and weekly economic time series," Discussion Papers 08/2025, Deutsche Bundesbank.
    10. A. Smyk & K. Webel, 2024. "Vers une désaisonnalisation des séries temporelles infra-mensuelles avec JDemetra+," Documents de Travail de l'Insee - INSEE Working Papers m2024-04, Institut National de la Statistique et des Etudes Economiques.
    11. 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.
    12. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.

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