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Real Time Analysis Based on Reproducing Kernel Henderson Filters/Análisis en tiempo real basado en la reproducción de los filtros de núcleo de Henderson



    () (Department of Statistics, University of Bologna. Italy.)


    () (Statistics Canada. Business Survey Methods Division (BSMD))


Recently, reproducing kernel Hilbert spaces have been introduced to provide a common approach for studying several nonparametric estimators used for smoothing functional time series data (Dagum and Bianconcini, 2006 and 2008). The reproducing kernel representation is based on the derivation of the density function (i.e. a second order kernel) embedded on the linear filter. This is the starting point for deriving higher order kernels, which are obtained from the product of the density and its orthonormal polynomials. This paper focuses on the Henderson filter, for which two density functions and corresponding hierarchies have been derived. The properties of the Henderson reproducing kernels are analyzed when the filters are adapted at the end of the sample period. The optimality criterion satisfied as well as the influence of the kernel order and bandwidth parameter are studied. Recientemente, la reproducción de los espacios de núcleo (kernel) de Hilbert se ha ido extendiendo con el objetivo de proporcionar un enfoque común para estudiar diversos estimadores no paramétricos de alisado para datos de series temporales funcionales (Dagum y Bianconcini, 2006 y 2008). La representación del núcleo reproducido se basa en la obtención de la función de densidad (i.e., un núcleo (kernel) de segundo orden) incluido en el filtro linear. Esto constituye el punto de partida para derivar núcleos de orden superior, obtenidos a partir del producto de la densidad por sus polinomios ortonormales. Este artículo se centra en el filtro de Henderson, para el que se obtienen dos funciones de densidad y sus correspondientes jerarquías. Se analizan las propiedades de los núcleos de Henderson reproducidos cuando se adaptan los filtros al final del período muestral. Además, se estudia el criterio de optimalidad que satisfacen así como la influencia del orden del núcleo y del parámetro del ancho de banda.

Suggested Citation

  • 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 Economía Aplicada, Estudios de Economía Aplicada, vol. 28, pages 553-574, Diciembre.
  • Handle: RePEc:lrk:eeaart:28_3_3

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    References listed on IDEAS

    1. 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.
    2. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-152, April.
    3. 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.
    4. Estela Bee Dagum & Silvia Bianconcini, 2013. "A Unified View of Nonparametric Trend-Cycle Predictors Via Reproducing Kernel Hilbert Spaces," Econometric Reviews, Taylor & Francis Journals, vol. 32(7), pages 848-867, October.
    5. 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.
    6. Wallis, Kenneth F, 1981. "Models for X-11 and 'X-11-Forecast' Procedures for Preliminary and Revised Seasonal Adjustments," The Warwick Economics Research Paper Series (TWERPS) 198, University of Warwick, Department of Economics.
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    More about this item


    Filtro de Henderson; Espacios de núcleo de Hilbert; estimadores de alisado. ; Henderson Filters; Kernel Hilbert spaces; smoothing estimators.;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models


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