IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

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

Listed author(s):
  • Agustín Maravall

    ()

    (Banco de España)

  • Ana del Río

    ()

    (Banco de España)

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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/07/Fic/dt0728e.pdf
File Function: First version, September 2007
Download Restriction: no

Paper provided by Banco de España & Working Papers Homepage in its series Working Papers with number 0728.

as
in new window

Length: 45 pages
Date of creation: Sep 2007
Handle: RePEc:bde:wpaper:0728
Contact details of provider: Web page: http://www.bde.es/

Web page: http://www.bde.es/bde/en/secciones/informes/Publicaciones_se/docs/
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as
in new window


  1. Maravall, Agustin & Mathis, Alexandre, 1994. "Encompassing univariate models in multivariate time series : A case study," Journal of Econometrics, Elsevier, vol. 61(2), pages 197-233, April.
  2. Donato Masciandaro & María J. Nieto & Henriëtte Prast, 2007. "Financial governance of banking supervision," Working Papers 0725, Banco de España;Working Papers Homepage.
  3. Maravall, Agustin, 2006. "An application of the TRAMO-SEATS automatic procedure; direct versus indirect adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2167-2190, May.
  4. Philip Vermeulen & Daniel A. Dias & Maarten Dossche & Erwan Gautier & Ignacio Hernando & Roberto Sabbatini & Harald Stahl, 2012. "Price Setting in the Euro Area: Some Stylized Facts from Individual Producer Price Data," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(8), pages 1631-1650, December.
  5. J. Durbin & S. J. Koopman, 2000. "Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 3-56.
  6. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-247, July-Sept.
  7. Philip Vermeulen & Daniel A. Dias & Maarten Dossche & Erwan Gautier & Ignacio Hernando & Roberto Sabbatini & Harald Stahl, 2012. "Price Setting in the Euro Area: Some Stylized Facts from Individual Producer Price Data," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(8), pages 1631-1650, December.
  8. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
  9. León, à ngel & Mencía, Javier & Sentana, Enrique, 2009. "Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 176-192.
  10. Mario Izquierdo & Juan Jimeno & Juan Rojas, 2010. "On the aggregate effects of immigration in Spain," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 1(4), pages 409-432, September.
  11. Cogley, Timothy, 2001. "Alternative definitions of the business cycle and their implications for business cycle models: A reply to Torben Mark Pederson," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1103-1107, August.
  12. Juan J. Dolado & Miguel Sebastián & Javier Vallés, 1993. "Ciclical patterns of the spanish economy," Investigaciones Economicas, Fundación SEPI, vol. 17(3), pages 445-473, September.
  13. Pollock, D.S.G., 2006. "Econometric methods of signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2268-2292, May.
  14. Claudia Canals & Xavier Gabaix & Josep M. Vilarrubia & David Weinstein, 2007. "Trade patterns, trade balances and idiosyncratic shocks," Working Papers 0721, Banco de España;Working Papers Homepage.
  15. Josep M. Vilarrubia, 2006. "Neighborhood effects in economic growth," Working Papers 0627, Banco de España;Working Papers Homepage.
  16. Kaiser, Regina & Maravall, Agustin, 2005. "Combining filter design with model-based filtering (with an application to business-cycle estimation)," International Journal of Forecasting, Elsevier, vol. 21(4), pages 691-710.
  17. Cooley, Thomas F. & Ohanian, Lee E., 1991. "The cyclical behavior of prices," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 25-60, August.
  18. Ghysels, Eric & Granger, Clive W J & Siklos, Pierre L, 1996. "Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process?," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 374-386, July.
  19. Harvey, Andrew, 1997. "Trends, Cycles and Autoregressions," Economic Journal, Royal Economic Society, vol. 107(440), pages 192-201, January.
  20. Andres, Javier & Domenech, Rafael & Fatas, Antonio, 2008. "The stabilizing role of government size," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 571-593, February.
  21. Eva Ortega & Eva Ferraz & Samuel Hurtado, 2007. "Actualización del modelo trimestral del Banco de España," Boletín Económico, Banco de España;Boletín Económico Homepage, issue JUN, Junio.
  22. Juan Ayuso & Juan F. Jimeno & Ernesto Villanueva, 2007. "The effects of the introduction of tax incentives on retirement savings," Working Papers 0724, Banco de España;Working Papers Homepage.
  23. Canova, Fabio, 1998. "Detrending and business cycle facts: A user's guide," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 533-540, May.
  24. Ricardo Gimeno & Juan M. Nave, 2006. "Genetic algorithm estimation of interest rate term structure," Working Papers 0634, Banco de España;Working Papers Homepage.
  25. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
  26. Cogley, Timothy & Nason, James M., 1995. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 253-278.
  27. Brewer, K. R. W., 1973. "Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models," Journal of Econometrics, Elsevier, vol. 1(2), pages 133-154, June.
  28. Juan Ruiz & Josep M. Vilarrubia, 2007. "The wise use of dummies in gravity models: export potentials in the Euromed region," Working Papers 0720, Banco de España;Working Papers Homepage.
  29. Morten O. Ravn & Harald Uhlig, 2002. "On adjusting the Hodrick-Prescott filter for the frequency of observations," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 371-375.
  30. Backus, David K & Kehoe, Patrick J, 1992. "International Evidence of the Historical Properties of Business Cycles," American Economic Review, American Economic Association, vol. 82(4), pages 864-888, September.
  31. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
  32. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
  33. Wynne, Mark A. & Koo, Jahyeong, 1997. "Business cycles under monetary union: EU and US business cycles compared," Working Papers 9707, Federal Reserve Bank of Dallas.
  34. Luis J. Álvarez & Ignacio Hernando, 2006. "Competition and price adjustment in the euro area," Working Papers 0629, Banco de España;Working Papers Homepage.
  35. Enrique Alberola & José María Serena, 2007. "Global financial integration, monetary policy and reserve accumulation. Assessing the limits in emerging economies," Working Papers 0706, Banco de España;Working Papers Homepage.
  36. Claude Giorno & Pete Richardson & Deborah Roseveare & Paul van den Noord, 1995. "Estimating Potential Output, Output Gaps and Structural Budget Balances," OECD Economics Department Working Papers 152, OECD Publishing.
  37. Pollock, D. S. G., 2003. "Improved frequency selective filters," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 279-297, March.
  38. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Working Papers 0108, Banco de España;Working Papers Homepage.
  39. Proietti, Tommaso, 2005. "New algorithms for dating the business cycle," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 477-498, April.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:bde:wpaper:0728. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (María Beiro. Electronic Dissemination of Information Unit. Research Department. Banco de España)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.