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Multivariate Trend–Cycle Extraction With The Hodrick–Prescott Filter

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  • Poloni, Federico
  • Sbrana, Giacomo

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.

Suggested Citation

  • Poloni, Federico & Sbrana, Giacomo, 2017. "Multivariate Trend–Cycle Extraction With The Hodrick–Prescott Filter," Macroeconomic Dynamics, Cambridge University Press, vol. 21(6), pages 1336-1360, September.
    • Handle: RePEc:cup:macdyn:v:21:y:2017:i:06:p:1336-1360_00
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    Cited by:

    1. Sbrana, Giacomo & Silvestrini, Andrea & Venditti, Fabrizio, 2017. "Short-term inflation forecasting: The M.E.T.A. approach," International Journal of Forecasting, Elsevier, vol. 33(4), pages 1065-1081.
    2. Poloni, Federico & Sbrana, Giacomo, 2019. "Closed-form results for vector moving average models with a univariate estimation approach," Econometrics and Statistics, Elsevier, vol. 10(C), pages 27-52.
    3. Martin Boďa & Mariana Považanová, 2023. "How credible are Okun coefficients? The gap version of Okun’s law for G7 economies," Economic Change and Restructuring, Springer, vol. 56(3), pages 1467-1514, June.

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