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

Author

Listed:
  • 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.

Suggested Citation

  • Agustín Maravall & Ana del Río, 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Working Papers 0728, Banco de España;Working Papers Homepage.
  • Handle: RePEc:bde:wpaper:0728
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    References listed on IDEAS

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    Cited by:

    1. Terence C. Mills, 2013. "Trends, cycles and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 3, pages 45-60 Edward Elgar Publishing.
    2. Andreas Billmeier, 2009. "Ghostbusting: which output gap really matters?," International Economics and Economic Policy, Springer, vol. 6(4), pages 391-419, December.
    3. 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.
    4. 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.
    5. 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.
    6. Moghtaderi, Azadeh & Flandrin, Patrick & Borgnat, Pierre, 2013. "Trend filtering via empirical mode decompositions," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 114-126.
    7. Jaqueson K. Galimberti & Marcelo L. Moura, 2011. "Improving the reliability of real-time Hodrick-Prescott filtering using survey forecasts," Centre for Growth and Business Cycle Research Discussion Paper Series 159, Economics, The Univeristy of Manchester.
    8. Sbrana, Giacomo, 2013. "The exact linkage between the Beveridge–Nelson decomposition and other permanent-transitory decompositions," Economic Modelling, Elsevier, vol. 30(C), pages 311-316.
    9. 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.
    10. Victor M. Guerrero, 2008. "Estimating Trends with Percentage of Smoothness Chosen by the User," International Statistical Review, International Statistical Institute, vol. 76(2), pages 187-202, August.
    11. Aliaga Lordemann, Javier & Rubin de Celis, Raúl & Villegas Quino, Horacio, 2011. "No Linealidad de los Ciclos Económicos en Bolivia," Documentos de trabajo 7/2011, Instituto de Investigaciones Socio-Económicas (IISEC), Universidad Católica Boliviana.
    12. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    13. Galimberti, Jaqueson K. & Moura, Marcelo L., 2016. "Improving the reliability of real-time output gap estimates using survey forecasts," International Journal of Forecasting, Elsevier, vol. 32(2), pages 358-373.
    14. Tapia, Jose, 2016. "Oil prices and the world business cycle: A causal investigation," MPRA Paper 68978, University Library of Munich, Germany.

    More about this item

    Keywords

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

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E66 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - General Outlook and Conditions

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