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Seasonal modulation mixed models for time series forecasting

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  • Lee, Dae-Jin
  • Durbán, María

Abstract

We propose an extension of a seasonal modulation smooth model with P-splines for times series data using a mixed model formulation. A smooth trend with seasonality decomposition can be estimated simultaneously. We extend the model to consider the forecasting of new future observations in the mixed model framework. Two different approaches are used for forecasting in the context of mixed models, and the equivalence of both methods is shown. The methodology is illustrated with monthly sulphur dioxide (SO2) levels in a selection of monitoring sites in Europe from January 1990 to December 2001.

Suggested Citation

  • Lee, Dae-Jin & Durbán, María, 2012. "Seasonal modulation mixed models for time series forecasting," DES - Working Papers. Statistics and Econometrics. WS ws122519, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws122519
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    References listed on IDEAS

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    1. I. D. Currie & M. Durban & P. H. C. Eilers, 2006. "Generalized linear array models with applications to multidimensional smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 259-280, April.
    2. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    3. Gilmour, Arthur & Cullis, Brian & Welham, Sue & Gogel, Beverley & Thompson, Robin, 2004. "An efficient computing strategy for prediction in mixed linear models," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 571-586, January.
    4. Maria Durbán & Iain D. Currie, 2003. "A note on P-spline additive models with correlated errors," Computational Statistics, Springer, vol. 18(2), pages 251-262, July.
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    Cited by:

    1. Marra, Giampiero & Radice, Rosalba, 2017. "Bivariate copula additive models for location, scale and shape," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 99-113.

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    Varying-coefficient models;

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