IDEAS home Printed from https://ideas.repec.org/a/eee/intfor/v21y2005i4p691-710.html
   My bibliography  Save this article

Combining filter design with model-based filtering (with an application to business-cycle estimation)

Author

Listed:
  • Kaiser, Regina
  • Maravall, Agustin

Abstract

Filters used to estimate unobserved components in time series are often designed on a priori grounds, so as to capture the frequencies associated with the component. A limitation of these filters is that they may yield spurious results. The danger can be avoided if the so called ARIMA model based (AMB) procedure is used to derive the filter. However, parsimony of ARIMA models typically implies little resolution in terms of the detection of hidden components. It would be desirable to combine a higher resolution with consistency with the structure of the observed series. We show first that for a large class of a priori designed filters, an AMB interpretation is always possible. Using this result, proper convolution of AMB filters can produce richer decompositions of the series that incorporate a priori desired features for the components, and fully respect the ARIMA model for the observed series. (Hence no additional parameter needs to be estimated.) The procedure is discussed in detail in the context of business cycle estimation by means of the Hodrick Prescott filter applied to a seasonally adjusted series or a trend cycle component.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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.
    • Handle: RePEc:eee:intfor:v:21:y:2005:i:4:p:691-710
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0169-2070(05)00053-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Burridge, Peter & Wallis, Kenneth F, 1984. "Unobserved-Components Models for Seasonal Adjustment Filters," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 350-359, October.
    2. 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.
    3. David A. Pierce, 1978. "Seasonal Adjustment When Both Deterministic and Stochastic Seasonality Are Present," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 242-280, National Bureau of Economic Research, Inc.
    4. Gersch, Will & Kitagawa, Genshiro, 1983. "The Prediction of Time Series with Trends and Seasonalities," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(3), pages 253-264, July.
    5. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
    6. Arnold Zellner, 1978. "Seasonal Analysis of Economic Time Series," NBER Books, National Bureau of Economic Research, Inc, number zell78-1, March.
    7. 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.
    8. Nerlove, Marc & Grether, David M. & Carvalho, José L., 1979. "Analysis of Economic Time Series," Elsevier Monographs, Elsevier, edition 1, number 9780125157506 edited by Shell, Karl.
    9. 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.
    10. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Time Series: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 343-349, October.
    11. Victor Gómez & Agustín Maravall, 1996. "Programs TRAMO and SEATS, Instruction for User (Beta Version: september 1996)," Working Papers 9628, Banco de España.
    12. Maravall, Agustin, 1985. "On Structural Time Series Models and the Characterization of Components," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(4), pages 350-355, October.
    13. E. J. Working, 1927. "What Do Statistical "Demand Curves" Show?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 41(2), pages 212-235.
    14. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
    15. 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.
    16. Pollock, D. S. G., 2003. "Improved frequency selective filters," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 279-297, March.
    17. Pollock, D. S. G., 2000. "Trend estimation and de-trending via rational square-wave filters," Journal of Econometrics, Elsevier, vol. 99(2), pages 317-334, December.
    18. David A. Pierce, 1978. "Seasonal adjustment when both deterministic and stochastic seasonality are present," Special Studies Papers 107, Board of Governors of the Federal Reserve System (U.S.).
    19. Finn E. Kydland & Edward C. Prescott, 1990. "Business cycles: real facts and a monetary myth," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 14(Spr), pages 3-18.
    20. 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.
    21. Robert F. Engle, 1978. "Estimating Structural Models of Seasonality," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 281-308, National Bureau of Economic Research, Inc.
    22. 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.
    23. Maravall, Agustin, 1988. "A note on minimum mean squared error estimation of signals with unit roots," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 589-593.
    24. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Working Papers 0108, Banco de España.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tommaso Proietti & Alberto Musso, 2012. "Growth accounting for the euro area," Empirical Economics, Springer, vol. 43(1), pages 219-244, August.
    2. Kamilya Tazhibayeva & Mr. Aasim M. Husain & Anna Ter-Martirosyan, 2008. "Fiscal Policy and Economic Cycles in Oil-Exporting Countries," IMF Working Papers 2008/253, International Monetary Fund.
    3. Maria Gadea & Ana Gómez-Loscos & Antonio Montañés, 2012. "Cycles inside cycles: Spanish regional aggregation," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(4), pages 423-456, December.
    4. Tommaso Proietti, 2009. "On the Model-Based Interpretation of Filters and the Reliability of Trend-Cycle Estimates," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 186-208.
    5. Maravall, A. & del Rio, A., 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 975-998, October.
    6. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    7. Acevedo Rueda, Rafael Alexis & Mora Mora, José U. & Harmath Fernández, Pedro Alexander, 2012. "La brecha del producto y el producto potencial en Venezuela: una estimación SVAR [Output Gap and Potential GDP in Venezuela: A SVAR Estimation]," MPRA Paper 58691, University Library of Munich, Germany, revised 2013.
    8. Guy Mélard, 2016. "On some remarks about SEATS signal extraction," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 53-98, March.
    9. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    10. Agustín Maravall Herrero & Domingo Pérez Cañete, 2011. "Applying and interpreting model-based seasonal adjustment. The euro-area industrial production series," Working Papers 1116, Banco de España.
    11. Julio Roman, Juan Manuel, 2011. "The Hodrick-Prescott filter with priors: linear restrictions on HP filters," MPRA Paper 34202, University Library of Munich, Germany.
    12. Peña, Daniel, 2020. "Agustín Maravall: An interview with the International Journal of Forecasting," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1241-1251.
    13. Tommaso Proietti, 2012. "Seasonality, Forecast Extensions And Business Cycle Uncertainty," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 555-569, September.
    14. Tommaso Proietti, 2009. "Structural Time Series Models for Business Cycle Analysis," Palgrave Macmillan Books, in: Terence C. Mills & Kerry Patterson (ed.), Palgrave Handbook of Econometrics, chapter 9, pages 385-433, Palgrave Macmillan.
    15. McElroy Tucker S. & Maravall Agustin, 2014. "Optimal Signal Extraction with Correlated Components," Journal of Time Series Econometrics, De Gruyter, vol. 6(2), pages 1-37, July.
    16. Juan Manuel Julio, 2011. "Data Revisions and the Output Gap," Borradores de Economia 7956, Banco de la Republica.
    17. 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.
    18. Terence C. Mills, 2013. "Trends, cycles and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 3, pages 45-60, Edward Elgar Publishing.
    19. Dias, Maria Helena Ambrosio & Dias, Joilson, 2010. "Measuring the Cyclical Component of a Time Series: a New Proposed Methodology," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 30(1), October.
    20. Terence C. Mills, 2013. "Constructing U.K. Core Inflation," Econometrics, MDPI, vol. 1(1), pages 1-21, April.
    21. Musso, Alberto & Proietti, Tommaso, 2007. "Growth accounting for the euro area: a structural approach," Working Paper Series 804, European Central Bank.

    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. Kaiser Remiro, Regina & Maravall, Agustín, 1999. "Short-term and long-term trends, seasonal and the business cycle," DES - Working Papers. Statistics and Econometrics. WS 6291, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Regina Kaiser & Agustín Maravall, 2002. "A Complete Model-Based Interpretation of the Hodrick-Prescott Filter: Spuriousness Reconsidered," Working Papers 0208, Banco de España.
    3. Maravall, A. & del Rio, A., 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 975-998, October.
    4. Tommaso Proietti, 2012. "Seasonality, Forecast Extensions And Business Cycle Uncertainty," Journal of Economic Surveys, Wiley Blackwell, vol. 26(4), pages 555-569, September.
    5. Tawadros, George B., 2011. "The stylised facts of Australia's business cycle," Economic Modelling, Elsevier, vol. 28(1), pages 549-556.
    6. 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.
    7. Aadland, David, 2005. "Detrending time-aggregated data," Economics Letters, Elsevier, vol. 89(3), pages 287-293, December.
    8. 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.
    9. 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.
    10. Maravall, Agustin & Planas, Christophe, 1999. "Estimation error and the specification of unobserved component models," Journal of Econometrics, Elsevier, vol. 92(2), pages 325-353, October.
    11. 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.
    12. Roberto Iannaccone & Edoardo Otranto, 2003. "Signal Extraction in Continuous Time and the Generalized Hodrick- Prescott Filter," Econometrics 0311002, University Library of Munich, Germany.
    13. Paolo Guarda, 2002. "Potential output and the output gap in Luxembourg: some alternative methods," BCL working papers 4, Central Bank of Luxembourg.
    14. 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.
    15. Zsolt Darvas & Gábor Vadas, 2003. "Univariate Potential Output Estimations for Hungary," MNB Working Papers 2003/8, Magyar Nemzeti Bank (Central Bank of Hungary).
    16. João Valle e Azevedo, 2002. "Business Cycles: Cyclical Comovement Within the European Union in the Period 1960-1999. A Frequency Domain Approach," Working Papers w200205, Banco de Portugal, Economics and Research Department.
    17. Uhlig, H.F.H.V.S. & Ravn, M., 1997. "On Adjusting the H-P Filter for the Frequency of Observations," Other publications TiSEM 1dd22a17-bed0-4e7c-a2c1-d, Tilburg University, School of Economics and Management.
    18. Woitek, Ulrich, 2003. "Height cycles in the 18th and 19th centuries," Economics & Human Biology, Elsevier, vol. 1(2), pages 243-257, June.
    19. Ard den Reijer, 2006. "The Dutch business cycle: which indicators should we monitor?," DNB Working Papers 100, Netherlands Central Bank, Research Department.
    20. 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.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

    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:eee:intfor:v:21:y:2005:i:4:p:691-710. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijforecast .

    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.