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Instant Trend-Seasonal Decomposition of Time Series with Splines

Author

Listed:
  • Luis Francisco Rosales

    (Georg-August-University Göttingen)

  • Tatyana Krivobokova

    (Georg-August-University Göttingen)

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.

Suggested Citation

  • Luis Francisco Rosales & Tatyana Krivobokova, 2012. "Instant Trend-Seasonal Decomposition of Time Series with Splines," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 131, Courant Research Centre PEG.
  • Handle: RePEc:got:gotcrc:131
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    File URL: http://www2.vwl.wiso.uni-goettingen.de/courant-papers/CRC-PEG_DP_131.pdf
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    References listed on IDEAS

    as
    1. Pollock, D.S.G., 2006. "Econometric methods of signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2268-2292, May.
    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. 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.
    4. 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.
    5. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    6. 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.
    7. Kauermann Goeran & Krivobokova Tatyana & Semmler Willi, 2011. "Filtering Time Series with Penalized Splines," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-28, March.
    8. 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.
    9. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, January.
    10. Dermot J. Hayes & Andrew Schmitz, 1987. "Hog Cycles and Countercyclical Production Response," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 69(4), pages 762-770.
    11. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    12. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, January.
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    More about this item

    Keywords

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

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