Estimation error and the specification of unobserved component models

• Autores: Christophe Planas, Agustín Maravall
• Localización: Documentos de trabajo - Banco de España, ISSN 0213-2710, Nº 8, 1996, págs. 7-44
• Idioma: inglés
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• Resumen

  • The paper deals with the problem of identifying stochastic unobserved twocomponent models, as in seasonal adjustment or trend-cycle decompositions. Solutions based on the properties of the unobserved component estimation error are considered, and analytical expressions for the variances and covariances of the different types of estimation errors (errors in the final, preliminary. and concurrent estimator and in the forecast) are obtained for any admissible decomposition. These expressions are relatively simple and straightforwardly derived from the ARlMA. model for the observed series. It is shown that, in all cases, the estimation error variance is minimized at a canonical decomposition (Le., at a decomposition with one of the components noninvertible), and a procedure to determine that decomposition is presented. On occasion, however, the most precise final estimator is obtained at a canonical decomposition different from the one that yields the most precise preliminary estimator.

    Three examples illustrate the results and the computational algorithms. The first and second examples are based on the so-called Structural Time Series Model and ARIMA Model Based approaches, respectively. The third example is a class of models often encountered in actual time series.