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Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter

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  • Agustín Maravall

    ()
    (Banco de España)

  • Ana del Río

    ()
    (Banco de España)

Abstract

Maravall and del Río (2001), analized the time aggregation properties of the Hodrick-Prescott (HP) filter, which decomposes a time series into trend and cycle, for the case of annual, quarterly, and monthly data, and showed that aggregation of the disaggregate component cannot be obtained as the exact result from direct application of an HP filter to the aggregate series. The present paper shows how, using several criteria, one can find HP decompositions for different levels of aggregation that provide similar results. We use as the main criterion for aggregation the preservation of the period associated with the frequency for which the filter gain is ½; this criterion is intuitive and easy to apply. It is shown that the Ravn and Uhlig (2002) empirical rule turns out to be a first-order approximation to our criterion, and that alternative —more complex— criteria yield similar results. Moreover, the values of the parameter ? of the HP filter, that provide results that are approximately consistent under aggregation, are considerably robust with respect to the ARIMA model of the series. Aggregation is seen to work better for the case of temporal aggregation than for systematic sampling. Still a word of caution is made concerning the desirability of exact aggregation consistency. The paper concludes with a clarification having to do with the questionable spuriousness of the cycles obtained with HP filter.

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Bibliographic Info

Paper provided by Banco de Espa�a in its series Banco de Espa�a Working Papers with number 0728.

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Length: 45 pages
Date of creation: Sep 2007
Date of revision:
Handle: RePEc:bde:wpaper:0728

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Keywords: Time series; Filtering and Smoothing; Time aggregation; Trend estimation; Business cycles; ARIMA models;

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References

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Cited by:
  1. Andreas Billmeier, 2009. "Ghostbusting: which output gap really matters?," International Economics and Economic Policy, Springer, vol. 6(4), pages 391-419, December.
  2. Carlo Ciccarelli & Stefano Fenoaltea & Tommaso Proietti, 2010. "The effects of unification: markets, policy, and cyclical convergence in Italy, 1861–1913," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 4(3), pages 269-292, October.
  3. Carl Chiarella & Hing Hung & Thuy-Duong To, 2005. "The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach," Research Paper Series 151, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Kathavate, Jay, 2013. "Direct & Indirect Effects of Aid Volatility on Growth: Do Stronger Institutions Play a Role?," MPRA Paper 45187, University Library of Munich, Germany.
  5. Mikko Myrskylä, 2010. "The effects of shocks in early life mortality on later life expectancy and mortality compression: A cohort analysis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 22(12), pages 289-320, March.
  6. Aliaga Lordemann, Javier & Villegas Quino, Horacio & Rubín de Celis, Raúl, 2011. "Ciclos Económicos e Inversión en Bolivia," Documentos de trabajo 2/2011, Instituto de Investigaciones Socio-Económicas (IISEC), Universidad Católica Boliviana.

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