Linear dynamic harmonic regression

  • Authors:
  • Marcos Bujosa;Antonio García-Ferrer;Peter C. Young

  • Affiliations:
  • Dpto. de Fundamentos del Análisis Económico II, Universidad Complutense de Madrid, Somosaguas, 28223 Madrid, Spain;Dpto. de Análisis Económico: Economía Cuantitativa, Universidad Autónoma de Madrid, Cantoblanco, 28034 Madrid, Spain;Centre for Research on Environmental Systems and Statistics, Lancaster University, Lancaster LA1 4YQ, UK and Integrated Catchment Assessment and Management Centre, Australian National University, ...

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2007

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Abstract

Among the alternative unobserved components formulations within the stochastic state space setting, the dynamic harmonic regression (DHR) model has proven to be particularly useful for adaptive seasonal adjustment, signal extraction, forecasting and back-casting of time series. First, it is shown how to obtain AutoRegressive moving average (ARMA) representations for the DHR components under a generalized random walk setting for the associated stochastic parameters; a setting that includes several well-known random walk models as special cases. Later, these theoretical results are used to derive an alternative algorithm, based on optimization in the frequency domain, for the identification and estimation of DHR models. The main advantages of this algorithm are linearity, fast computational speed, avoidance of some numerical issues, and automatic identification of the DHR model. The signal extraction performance of the algorithm is evaluated using empirical applications and comprehensive Monte Carlo simulation analysis.