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

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

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Marcos Bujosa (Dpto. de Fundamentos del Análisis Económico II. Universidad Complutense de Madrid. Somosaguas,)
Antonio García Ferrer (Dpto. de Análisis Económico: Economía cuantitativa. Universidad Autónoma de Madrid)
Peter Young

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Marcos Bujosa

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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Paper provided by Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales in its series Documentos del Instituto Complutense de Análisis Económico with number 0204.

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Date of creation: 2002
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Handle: RePEc:ucm:doicae:0204

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This paper has been announced in the following NEP Reports:

NEP-ALL-2003-10-20 (All new papers)
NEP-CMP-2003-10-20 (Computational Economics)
NEP-ECM-2003-10-20 (Econometrics)
NEP-ETS-2003-10-20 (Econometric Time Series)

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Maravall, Agustin, 1993. "Stochastic linear trends : Models and estimators," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 5-37, March. [Downloadable!] (restricted)
Peter Young, 1999. "Recursive and en-bloc approaches to signal extraction," Journal of Applied Statistics, Taylor and Francis Journals, vol. 26(1), pages 103-128, January. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)

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