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An ARMA Representation of Unobserved Component Models under Generalized Random Walk Specifications: New Algorithms and Examples

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Abstract

Among the alternative Unobserved Components formulations within the stochastic state space setting, the Dynamic Harmonic Regression (DHR) has proved particularly useful for adaptive seasonal adjustment signal extraction, forecasting and back-casting of time series. Here, we show first how to obtain ARMA representations for the Dynamic Harmonic Regression (DHR) components under several random walk specifications. Later, we uses these theoretical results to derive an alternative algorithm based on the frequency domain for the identification and estimation of DHR models. The main advantages of this algorithm are linearity, fast computing, avoidance of some numerical issues, and automatic identification of the DHR model. To compare it with other alternatives, empirical applications are provided.

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  • 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.
  • Handle: RePEc:ucm:doicae:0204
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    1. Maravall, Agustin, 1993. "Stochastic linear trends : Models and estimators," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 5-37, March.
    2. Peter Young, 1999. "Recursive and en-bloc approaches to signal extraction," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(1), pages 103-128.
    3. Garcia-Ferrer, Antonio & Bujosa-Brun, Marcos, 2000. "Forecasting OECD industrial turning points using unobserved components models with business survey data," International Journal of Forecasting, Elsevier, vol. 16(2), pages 207-227.
    4. Andrés Bujosa & Marcos Bujosa & Antonio García Ferrer, 2002. "A Note on the Pseudo-Spectra and the Pseudo-Covariance Generating Functions of ARMA Processes," Documentos de Trabajo del ICAE 0203, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
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    Cited by:

    1. Garcia-Ferrer, A. & de Juan, A. & Poncela, P., 2006. "Forecasting traffic accidents using disaggregated data," International Journal of Forecasting, Elsevier, vol. 22(2), pages 203-222.
    2. Andrés Bujosa & Marcos Bujosa & Antonio García Ferrer, 2002. "A Note on the Pseudo-Spectra and the Pseudo-Covariance Generating Functions of ARMA Processes," Documentos de Trabajo del ICAE 0203, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    3. Gustavo A. Marrero, 2004. "Component versus Tradicional Models to Forecast Quarterly National Account Aggregates: a Monte Carlo Experiment," Documentos de Trabajo del ICAE 0410, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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