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

  • Maravall, A.
  • del Rio, A.

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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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 52 (2007)
Issue (Month): 2 (October)
Pages: 975-998

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Handle: RePEc:eee:csdana:v:52:y:2007:i:2:p:975-998
Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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  1. 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.
  2. 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.
  3. 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.
  4. Philip Vermeulen & Daniel Dias & Maarten Dossche & Erwan Gautier & Ignacio Hernando & Roberto Sabbatini & Harald Stahl, 2007. "Price setting in the euro area: some stylised facts from individual producer price data," Working Papers 0703, Banco de España;Working Papers Homepage.
  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. Timothy Cogley & James M. Nason, 1993. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series: implications for business cycle research," Working Papers in Applied Economic Theory 93-01, Federal Reserve Bank of San Francisco.
  7. 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.
  8. 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.
  9. David K. Backus & Patrick J. Kehoe, 1992. "International Evidence on the Historical Properties of Business Cycles," Working Papers 92-5, New York University, Leonard N. Stern School of Business, Department of Economics.
  10. Timothy Cogley, 1998. "Alternative definitions of the business cycle and their implications for business cycle models: a reply to Torben Mark Pederson," Working Papers in Applied Economic Theory 98-08, Federal Reserve Bank of San Francisco.
  11. Eva Ortega & Pablo Burriel & José Luis Fernández & Eva Ferraz & Samuel Hurtado, 2007. "Actualización del modelo trimestral del Banco de España," Working Papers 0717, Banco de España;Working Papers Homepage.
  12. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
  13. Ghysels, E. & Granger, C.W.J. & Siklos, P.L., 1995. "Is Seasonal Adjustment a Linear or Nonlinear Data Filtring Process," Cahiers de recherche 9517, Universite de Montreal, Departement de sciences economiques.
  14. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Canova, Fabio, 1998. "Detrending and business cycle facts: A user's guide," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 533-540, May.
  16. Harvey, Andrew, 1997. "Trends, Cycles and Autoregressions," Economic Journal, Royal Economic Society, vol. 107(440), pages 192-201, January.
  17. Javier Andrés & Rafael Doménech & Antonio Fatás, 2007. "The stabilizing role of government size," Working Papers 0710, Banco de España;Working Papers Homepage.
  18. Dias, D. & Dossche, M. & Gautier, E. & Hernando, I. & Sabbatini , R. & Stahl , H. & Vermeulen, P., 2007. "Macro Price setting in the euro area: Some stylised facts from Individual Producer Price," Working papers 164, Banque de France.
  19. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Working Papers 0108, Banco de España;Working Papers Homepage.
  20. Marianne Baxter & Robert G. King, 1995. "Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series," NBER Working Papers 5022, National Bureau of Economic Research, Inc.
  21. Cooley, T.F. & Ohanian, L.E., 1989. "The Cyclical Behavior Of Prices," RCER Working Papers 188, University of Rochester - Center for Economic Research (RCER).
  22. 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.
  23. Ángel León & Javier Mencía & Enrique Sentana, 2007. "Parametric properties of semi-nonparametric distributions, with applications to option valuation," Working Papers 0707, Banco de España;Working Papers Homepage.
  24. 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.
  25. Pollock, D. S. G., 2003. "Improved frequency selective filters," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 279-297, March.
  26. 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.
  27. Luis J. Álvarez & Ignacio Hernando, 2006. "Competition and price adjustment in the euro area," Working Papers 0629, Banco de España;Working Papers Homepage.
  28. 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.
  29. Regina Kaiser & Agustín Maravall, 2004. "Combining filter design with model based filtering (with an application to business cycle estimation)," Working Papers 0417, Banco de España;Working Papers Homepage.
  30. 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.
  31. Proietti, Tommaso, 2005. "New algorithms for dating the business cycle," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 477-498, April.
  32. Ricardo Gimeno & Juan M. Nave, 2006. "Genetic algorithm estimation of interest rate term structure," Working Papers 0634, Banco de España;Working Papers Homepage.
  33. 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.
  34. Pollock, D.S.G., 2006. "Econometric methods of signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2268-2292, May.
  35. 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.
  36. 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 231-47, July-Sept.
  37. 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.
  38. Josep M. Vilarrubia, 2006. "Neighborhood effects in economic growth," Working Papers 0627, Banco de España;Working Papers Homepage.
  39. Donato Masciandaro & María J. Nieto & Henriëtte Prast, 2007. "Financial governance of banking supervision," Working Papers 0725, Banco de España;Working Papers Homepage.
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