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. 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.
    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. Pollock, D. S. G., 2003. "Improved frequency selective filters," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 279-297, March.
    4. 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.
    5. 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.
    6. 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.
    7. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
    8. E. J. Working, 1927. "What Do Statistical "Demand Curves" Show?," The Quarterly Journal of Economics, Oxford University Press, vol. 41(2), pages 212-235.
    9. 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.
    10. 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.
    11. Robert F. Engle, 1979. "Estimating Structural Models of Seasonality," NBER Chapters,in: Seasonal Analysis of Economic Time Series, pages 281-308 National Bureau of Economic Research, Inc.
    12. 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.
    13. 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.).
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. Agustín Maravall & Ana del Río, 2001. "Time Aggregation and the Hodrick-Prescott Filter," Working Papers 0108, Banco de España;Working Papers Homepage.
    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. 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. Proietti, Tommaso, 2008. "Structural Time Series Models for Business Cycle Analysis," MPRA Paper 6854, University Library of Munich, Germany.
    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. 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;Working Papers Homepage.
    5. 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.
    6. Julio Roman, Juan Manuel, 2011. "The Hodrick-Prescott filter with priors: linear restrictions on HP filters," MPRA Paper 34202, University Library of Munich, Germany.
    7. Juan Manuel Julio, 2011. "Data Revisions and the Output Gap," Borradores de Economia 642, Banco de la Republica de Colombia.
    8. Kamilya Tazhibayeva & Aasim M. Husain & Anna Ter-Martirosyan, 2008. "Fiscal Policy and Economic Cycles in Oil-Exporting Countries," IMF Working Papers 08/253, International Monetary Fund.
    9. Terence C. Mills, 2013. "Constructing U.K. Core Inflation," Econometrics, MDPI, Open Access Journal, vol. 1(1), pages 1-21, April.
    10. repec:sbe:breart:v:30:y:2010:i:1:a:3503 is not listed on IDEAS
    11. Musso, Alberto & Proietti, Tommaso, 2007. "Growth accounting for the euro area: a structural approach," Working Paper Series 804, European Central Bank.
    12. 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.
    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. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.

    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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/ijforecast .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.