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The Henderson Smoother in Reproducing Kernel Hilbert Space

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  • Dagum, Estela Bee
  • Bianconcini, Silvia

Abstract

The Henderson smoother has been traditionally applied for trend-cycle estimation in the context of nonparametric seasonal adjustment software officially adopted by statistical agencies. This study introduces a Henderson third-order kernel representation by means of the reproducing kernel Hilbert space (RKHS) methodology. Two density functions and corresponding orthonormal polynomials have been calculated. Both are shown to give excellent representations for short- and medium-length filters. Theoretical and empirical comparisons of the Henderson third-order kernel asymmetric filters are made with the classical ones. The former are shown to be superior in terms of signal passing, noise suppression, and revision size.

Suggested Citation

  • Dagum, Estela Bee & Bianconcini, Silvia, 2008. "The Henderson Smoother in Reproducing Kernel Hilbert Space," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 536-545.
    • Handle: RePEc:bes:jnlbes:v:26:y:2008:p:536-545
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    Cited by:

    1. 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.
    2. 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.
    3. McElroy, Tucker S. & Jach, Agnieszka, 2023. "Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    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. Anusha, "undated". "Evaluating reliability of some symmetric and asymmetric univariate filters," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2015-030, Indira Gandhi Institute of Development Research, Mumbai, India.

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