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Recursive and en-bloc approaches to signal extraction

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  • Peter Young

Abstract

In the literature on unobservable component models , three main statistical instruments have been used for signal extraction: fixed interval smoothing (FIS), which derives from Kalman's seminal work on optimal state-space filter theory in the time domain; Wiener-Kolmogorov-Whittle optimal signal extraction (OSE) theory, which is normally set in the frequency domain and dominates the field of classical statistics; and regularization , which was developed mainly by numerical analysts but is referred to as 'smoothing' in the statistical literature (such as smoothing splines, kernel smoothers and local regression). Although some minor recognition of the interrelationship between these methods can be discerned from the literature, no clear discussion of their equivalence has appeared. This paper exposes clearly the interrelationships between the three methods; highlights important properties of the smoothing filters used in signal extraction; and stresses the advantages of the FIS algorithms as a practical solution to signal extraction and smoothing problems. It also emphasizes the importance of the classical OSE theory as an analytical tool for obtaining a better understanding of the problem of signal extraction.

Suggested Citation

  • Peter Young, 1999. "Recursive and en-bloc approaches to signal extraction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(1), pages 103-128.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:1:p:103-128
    DOI: 10.1080/02664769922692
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    1. Tych, Wlodek & Pedregal, Diego J. & Young, Peter C. & Davies, John, 2002. "An unobserved component model for multi-rate forecasting of telephone call demand: the design of a forecasting support system," International Journal of Forecasting, Elsevier, vol. 18(4), pages 673-695.
    2. Bujosa, Marcos & Garcia-Ferrer, Antonio & Young, Peter C., 2007. "Linear dynamic harmonic regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 999-1024, October.
    3. Tommaso Proietti, 2005. "Forecasting and signal extraction with misspecified models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(8), pages 539-556.
    4. García Márquez, Fausto Pedro & Schmid, Felix, 2007. "A digital filter-based approach to the remote condition monitoring of railway turnouts," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 830-840.
    5. Paredes, Joan & Pedregal, Diego J. & Pérez, Javier J., 2009. "A quarterly fiscal database for the euro area based on intra-annual fiscal information," Working Paper Series 1132, European Central Bank.
    6. Young, Peter C., 2018. "Data-based mechanistic modelling and forecasting globally averaged surface temperature," International Journal of Forecasting, Elsevier, vol. 34(2), pages 314-335.
    7. Theresa Maria Rausch & Tobias Albrecht & Daniel Baier, 2022. "Beyond the beaten paths of forecasting call center arrivals: on the use of dynamic harmonic regression with predictor variables," Journal of Business Economics, Springer, vol. 92(4), pages 675-706, May.
    8. Ombao, Hernando & Ringo Ho, Moon-ho, 2006. "Time-dependent frequency domain principal components analysis of multichannel non-stationary signals," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2339-2360, May.
    9. Paredes, Joan & Pedregal, Diego J. & Pérez, Javier J., 2014. "Fiscal policy analysis in the euro area: Expanding the toolkit," Journal of Policy Modeling, Elsevier, vol. 36(5), pages 800-823.
    10. Geraint Johnes, 2000. "Up Around the Bend: Linear and nonlinear models of the UK economy compared," International Review of Applied Economics, Taylor & Francis Journals, vol. 14(4), pages 485-493.
    11. Victor M. Guerrero, 2008. "Estimating Trends with Percentage of Smoothness Chosen by the User," International Statistical Review, International Statistical Institute, vol. 76(2), pages 187-202, August.
    12. Pedregal, Diego J. & Young, Peter C., 2006. "Modulated cycles, an approach to modelling periodic components from rapidly sampled data," International Journal of Forecasting, Elsevier, vol. 22(1), pages 181-194.
    13. Artis, Michael & Nachane, Dilip M & Hoffmann, Mathias & Clavel, Jose Garcia, 2007. "Analyzing Strongly Periodic Series in the Frequency Domain: A Comparison of Alternative Approaches with Applications," CEPR Discussion Papers 6517, C.E.P.R. Discussion Papers.
    14. Marcos Bujosa & Antonio García Ferrer & Peter Young, 2002. "An ARMA Representation of Unobserved Component Models under Generalized Random Walk Specifications: New Algorithms and Examples," Documentos de Trabajo del ICAE 0204, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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