IDEAS home Printed from https://ideas.repec.org/p/bde/wpaper/0728.html
   My bibliography  Save this paper

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.
  • Handle: RePEc:bde:wpaper:0728
    as

    Download full text from publisher

    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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Pollock, D.S.G., 2006. "Econometric methods of signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2268-2292, May.
    8. Claudia Canals & Xavier Gabaix & Josep M. Vilarrubia & David Weinstein, 2007. "Trade patterns, trade balances and idiosyncratic shocks," Working Papers 0721, Banco de España.
    9. Ghysels, Eric & Granger, Clive W J & Siklos, Pierre L, 1996. "Is Seasonal Adjustment a Linear or Nonlinear Data-Filtering Process? Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 396-397, July.
    10. Juan Ayuso & Juan F. Jimeno & Ernesto Villanueva, 2019. "The effects of the introduction of tax incentives on retirement saving," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 10(3), pages 211-249, November.
    11. 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.
    12. 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.
    13. Eva Ortega & Eva Ferraz & Samuel Hurtado, 2007. "Actualización del modelo trimestral del Banco de España," Boletín Económico, Banco de España, issue JUN, pages 55-65, Junio.
    14. Cooley, Thomas F. & Ohanian, Lee E., 1991. "The cyclical behavior of prices," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 25-60, August.
    15. 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.
    16. Canova, Fabio, 1998. "Detrending and business cycle facts: A user's guide," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 533-540, May.
    17. Donato Masciandaro & María J. Nieto & Henriëtte Prast, 2007. "Financial governance of banking supervision," Working Papers 0725, Banco de España.
    18. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. Tucker McElroy, 2008. "Exact formulas for the Hodrick-Prescott filter," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 209-217, March.
    25. 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.
    26. Luis J. Álvarez & Ignacio Hernando, 2006. "Competition and price adjustment in the euro area," Working Papers 0629, Banco de España.
    27. Pollock, D. S. G., 2003. "Improved frequency selective filters," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 279-297, March.
    28. 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.
    29. 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.
    30. 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.
    31. Daniel O. Stram & William W. S. Wei, 1986. "Temporal Aggregation In The Arima Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(4), pages 279-292, July.
    32. Josep M. Vilarrubia, 2006. "Neighborhood effects in economic growth," Working Papers 0627, Banco de España.
    33. Harvey, Andrew, 1997. "Trends, Cycles and Autoregressions," Economic Journal, Royal Economic Society, vol. 107(440), pages 192-201, January.
    34. Ricardo Gimeno & Juan M. Nave, 2006. "Genetic algorithm estimation of interest rate term structure," Working Papers 0634, Banco de España.
    35. 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.
    36. 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.
    37. 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.
    38. Jahyeong Koo & Mark A. Wynne, 1997. "Business cycles under monetary union: EU and US business cycles compared," Working Papers 9707, Federal Reserve Bank of Dallas.
    39. 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.
    40. 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.
    41. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Working Papers 0108, Banco de España.
    42. 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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Roberto Iannaccone & Edoardo Otranto, 2003. "Signal Extraction in Continuous Time and the Generalized Hodrick- Prescott Filter," Econometrics 0311002, University Library of Munich, Germany.
    2. Isabel Argimón & Pablo Hernández de Cos, 2008. "The determinants of budget balances of the regional (Autonomous) governments," Working Papers 0803, Banco de España.
    3. Aitor Erce, 2008. "A structural model of sovereign debt issuance: assessing the role of financial factors," Working Papers 0809, Banco de España.
    4. 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.
    5. Hall, Viv B & Thomson, Peter, 2022. "A boosted HP filter for business cycle analysis: evidence from New Zealand’s small open economy," Working Paper Series 9473, Victoria University of Wellington, School of Economics and Finance.
    6. Aadland, David, 2005. "Detrending time-aggregated data," Economics Letters, Elsevier, vol. 89(3), pages 287-293, December.
    7. David E. Giles & Chad N. Stroomer, 2004. "Identifying the Cycle of a Macroeconomic Time-Series Using Fuzzy Filtering," Econometrics Working Papers 0406, Department of Economics, University of Victoria.
    8. Tawadros, George B., 2011. "The stylised facts of Australia's business cycle," Economic Modelling, Elsevier, vol. 28(1), pages 549-556.
    9. Eduardo Loría & Emmanuel Salas, 2014. "Ciclos, crecimiento económico y crisis en México, 1980.1-2013.4," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 29(2), pages 131-161.
    10. 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.
    11. Viv B. Hall & Peter Thomson, 2022. "A boosted HP filter for business cycle analysis:evidence from New Zealand's small open economy," CAMA Working Papers 2022-45, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    12. Andrikopoulos, Andreas & Loizides, Ioannis & Prodromidis, Kyprianos, 2004. "Fiscal policy and political business cycles in the EU," European Journal of Political Economy, Elsevier, vol. 20(1), pages 125-152, March.
    13. Sunder, Marco & Woitek, Ulrich, 2005. "Boom, bust, and the human body: Further evidence on the relationship between height and business cycles," Economics & Human Biology, Elsevier, vol. 3(3), pages 450-466, December.
    14. Zacharias Psaradakis & Martin Sola, 2003. "On detrending and cyclical asymmetry," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(3), pages 271-289.
    15. Mertens, Elmar, 2010. "Structural shocks and the comovements between output and interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1171-1186, June.
    16. Uhlig, H.F.H.V.S. & Ravn, M., 1997. "On Adjusting the H-P Filter for the Frequency of Observations," Discussion Paper 1997-50, Tilburg University, Center for Economic Research.
    17. Álvarez, Luis J. & Gómez-Loscos, Ana, 2018. "A menu on output gap estimation methods," Journal of Policy Modeling, Elsevier, vol. 40(4), pages 827-850.
    18. Mark Meyer & Peter Winker*, 2005. "Using HP Filtered Data for Econometric Analysis: Some Evidence from Monte Carlo Simulations," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 89(3), pages 303-320, August.
    19. Movshuk, Oleksandr, 2003. "Does the choice of detrending method matter in demand analysis?," Japan and the World Economy, Elsevier, vol. 15(3), pages 341-359, August.
    20. Miroslav Plašil, 2011. "Potenciální produkt, mezera výstupu a míra nejistoty spojená s jejich určením při použití Hodrick-Prescottova filtru [Potential Product, Output Gap and Uncertainty Rate Associated with Their Determ," Politická ekonomie, Prague University of Economics and Business, vol. 2011(4), pages 490-507.

    More about this item

    Keywords

    Time series; Filtering and Smoothing; Time aggregation; Trend estimation; Business cycles; ARIMA models;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bde:wpaper:0728. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ángel Rodríguez. Electronic Dissemination of Information Unit. Research Department. Banco de España (email available below). General contact details of provider: https://edirc.repec.org/data/bdegves.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.