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MULTIVARIATE TREND–CYCLE EXTRACTION WITH THE HODRICK–PRESCOTT FILTER

  • Federico Poloni (a1) and Giacomo Sbrana (a2)
Abstract

The Hodrick–Prescott filter represents one of the most popular methods for trend–cycle extraction in macroeconomic time series. In this paper we provide a multivariate generalization of the Hodrick–Prescott filter, based on the seemingly unrelated time series approach. We first derive closed-form expressions linking the signal–noise matrix ratio to the parameters of the VARMA representation of the model. We then show that the parameters can be estimated using a recently introduced method, called “Moment Estimation Through Aggregation (META).” This method replaces traditional multivariate likelihood estimation with a procedure that requires estimating univariate processes only. This makes the estimation simpler, faster, and better behaved numerically. We prove that our estimation method is consistent and asymptotically normal distributed for the proposed framework. Finally, we present an empirical application focusing on the industrial production of several European countries.

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Corresponding author
Address correspondence to: Giacomo Sbrana, NEOMA Business School, 1 Rue du Marchal Juin, 76130 Mont-Saint-Aignan, France; e-mail: giacomo.sbrana@neoma-bs.fr.
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F. Poloni is partially supported by INDAM (Istituto Nazionale di Alta Matematica) and by a PRA project of the University of Pisa.

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Macroeconomic Dynamics
  • ISSN: 1365-1005
  • EISSN: 1469-8056
  • URL: /core/journals/macroeconomic-dynamics
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