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A Unified View of Nonparametric Trend-Cycle Predictors Via Reproducing Kernel Hilbert Spaces

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  • Estela Bee Dagum
  • Silvia Bianconcini

Abstract

We provide a common approach for studying several nonparametric estimators used for smoothing functional time series data. Linear filters based on different building assumptions are transformed into kernel functions via reproducing kernel Hilbert spaces. For each estimator, we identify a density function or second order kernel, from which a hierarchy of higher order estimators is derived. These are shown to give excellent representations for the currently applied symmetric filters. In particular, we derive equivalent kernels of smoothing splines in Sobolev and polynomial spaces. The asymmetric weights are obtained by adapting the kernel functions to the length of the various filters, and a theoretical and empirical comparison is made with the classical estimators used in real time analysis. The former are shown to be superior in terms of signal passing, noise suppression and speed of convergence to the symmetric filter.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:emetrv:v:32:y:2013:i:7:p:848-867
    DOI: 10.1080/07474938.2012.690674
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    Cited by:

    1. Dagum, Estela Bee, 2010. "Business Cycles and Current Economic Analysis/Los ciclos económicos y el análisis económico actual," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 28, pages 577-594, Diciembre.
    2. 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.
    3. 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.

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