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Instant Trend-Seasonal Decomposition of Time Series with Splines

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  • Luis Francisco Rosales

    (Georg-August-University Göttingen)

  • Tatyana Krivobokova

    (Georg-August-University Göttingen)

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    Abstract

    We present a nonparametric method to decompose a times series into trend, seasonal and remainder components. This fully data-driven technique is based on penalized splines and makes an explicit characterization of the varying seasonality and the correlation in the remainder. The procedure takes advantage of the mixed model representation of penalized splines that allows for the simultaneous estimation of all model parameters from the corresponding likelihood. Simulation studies and three data examples illustrate the eff ectiveness of the approach.

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    File URL: http://www2.vwl.wiso.uni-goettingen.de/courant-papers/CRC-PEG_DP_131.pdf
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    Bibliographic Info

    Paper provided by Courant Research Centre PEG in its series Courant Research Centre: Poverty, Equity and Growth - Discussion Papers with number 131.

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    Date of creation: 20 Nov 2012
    Date of revision:
    Handle: RePEc:got:gotcrc:131

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    Postal: Platz der Goettinger Sieben 3; D-37073 Goettingen, GERMANY
    Phone: +49 551 39 14066
    Fax: + 49 551 39 14059
    Web page: http://www.uni-goettingen.de/en/82144.html

    Related research

    Keywords: Penalized splines; Mixed model; Varying coecient; Correlated remainder;

    This paper has been announced in the following NEP Reports:

    References

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    1. 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 127-52, April.
    2. Tatyana Krivobokova, 2011. "Smoothing parameter selection in two frameworks for penalized splines," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 85, Courant Research Centre PEG, revised 18 Oct 2012.
    3. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    4. Pollock, D.S.G., 2006. "Econometric methods of signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2268-2292, May.
    5. Krivobokova, Tatyana & Kauermann, Goran, 2007. "A Note on Penalized Spline Smoothing With Correlated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1328-1337, December.
    6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    7. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    8. Hayes, Dermot J. & Schmitz, Andrew, 1987. "Hog Cycles and Countercyclical Production Response," Staff General Research Papers 597, Iowa State University, Department of Economics.
    9. Theodore Alexandrov & Silvia Bianconcini & Estela Bee Dagum & Peter Maass & Tucker S. McElroy, 2012. "A Review of Some Modern Approaches to the Problem of Trend Extraction," Econometric Reviews, Taylor & Francis Journals, vol. 31(6), pages 593-624, November.
    10. Delgado, Luis & Humala, Alberto, 1997. "El mercado bursátil peruano y la hipótesis del mercado eficiente," Revista Estudios Económicos, Banco Central de Reserva del Perú, issue 1, pages 73-92.
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