IDEAS home Printed from https://ideas.repec.org/p/fip/fedcwp/9906.html
   My bibliography  Save this paper

The Band pass filter

Author

Listed:
  • Lawrence J. Christiano
  • Terry J. Fitzgerald

Abstract

The \"ideal\" band-pass filter can be used to isolate the component of a time series that lies within a particular band of frequencies, but applying this filter requires a data set of infinite length. In practice, some sort of approximation is needed. Using projections, the authors derive approximations that are optimal when the time-series representations underlying the raw data have a unit root, or are stationary about a trend.

Suggested Citation

  • Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Papers (Old Series) 9906, Federal Reserve Bank of Cleveland.
  • Handle: RePEc:fip:fedcwp:9906
    as

    Download full text from publisher

    File URL: https://www.clevelandfed.org/~/media/content/newsroom%20and%20events/publications/working%20papers/1999/wp%209906%20the%20band%20pass%20filter%20pdf.pdf?la=en
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    • Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "The Band Pass Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 435-465, May.

    References listed on IDEAS

    as
    1. Prescott, Edward C., 1986. "Theory ahead of business-cycle measurement," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 11-44, January.
    2. Lawrence J. Christiano & Terry J. Fitzgerald, 1998. "The business cycle: it's still a puzzle," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 22(Q IV), pages 56-83.
    3. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64, Elsevier.
    4. William Poole, 1999. "Monetary policy rules?," Review, Federal Reserve Bank of St. Louis, issue Mar, pages 3-12.
    5. Chistiano, Lawrence J & den Haan, Wouter J, 1996. "Small-Sample Properties of GMM for Business-Cycle Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 309-327, July.
    6. 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.
    7. Robert J. Barro & David B. Gordon, 2019. "A Positive Theory of Monetary Policy in a Natural Rate Model," Credit and Capital Markets, Credit and Capital Markets, vol. 52(4), pages 505-525.
    8. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
    9. Christiano, Lawrence J. & Eichenbaum, Martin, 1990. "Unit roots in real GNP: Do we know, and do we care?," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 32(1), pages 7-61, January.
    10. Cooley, Thomas F. & Ohanian, Lee E., 1991. "The cyclical behavior of prices," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 25-60, August.
    11. Chari, V. V. & Christiano, Lawrence J. & Eichenbaum, Martin, 1998. "Expectation Traps and Discretion," Journal of Economic Theory, Elsevier, vol. 81(2), pages 462-492, August.
    12. Orphanides, Athanasios, 2003. "The quest for prosperity without inflation," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 633-663, April.
    13. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
    14. 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.
    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. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, December.
    17. Lucas, Robert E, Jr, 1980. "Two Illustrations of the Quantity Theory of Money," American Economic Review, American Economic Association, vol. 70(5), pages 1005-1014, December.
    18. Pierre St-Amant & Simon van Norden, 1997. "Measurement of the Output Gap: A Discussion of Recent Research at the Bank of Canada," Technical Reports 79, Bank of Canada.
    19. Ball, Laurence & Mankiw, N. Gregory, 1994. "A sticky-price manifesto," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 41(1), pages 127-151, December.
    20. Singleton, Kenneth J., 1988. "Econometric issues in the analysis of equilibrium business cycle models," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 361-386.
    21. Edmund S. Phelps, 1968. "Money-Wage Dynamics and Labor-Market Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 76, pages 678-678.
    22. Andreas Hornstein, 1998. "Inventory investment and the business cycle," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 49-71.
    23. Engle, Robert F, 1974. "Band Spectrum Regression," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 1-11, February.
    24. Ireland, Peter N., 1999. "Does the time-consistency problem explain the behavior of inflation in the United States?," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 279-291, October.
    25. Ireland, Peter N., 1997. "Sustainable monetary policies," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 87-108, November.
    26. Whiteman, Charles H, 1984. "Lucas on the Quantity Theory: Hypothesis Testing without Theory," American Economic Review, American Economic Association, vol. 74(4), pages 742-749, September.
    27. King, Robert G. & Watson, Mark W., 1994. "The post-war U.S. phillips curve: a revisionist econometric history," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 41(1), pages 157-219, December.
    28. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
    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. Lawrence J. Christiano & Christopher J. Gust, 2000. "The expectations trap hypothesis," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 25(Q II), pages 21-39.
    2. Orphanides, Athanasios & van Norden, Simon, 2005. "The Reliability of Inflation Forecasts Based on Output Gap Estimates in Real Time," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 583-601, June.
    3. de Carvalho, Miguel & Rua, António, 2017. "Real-time nowcasting the US output gap: Singular spectrum analysis at work," International Journal of Forecasting, Elsevier, vol. 33(1), pages 185-198.
    4. João Sousa Andrade & António Portugal Duarte, 2012. "The Importance of a Good Indicator for Global Exciess Demand," Book Chapters, in: Paulino Teixeira & António Portugal Duarte & Srdjan Redzepagic & Dejan Eric (ed.), European Integration Process in Western Balkan Countries, edition 1, volume 1, chapter 1, pages 11-35, Institute of Economic Sciences.
    5. João Sousa Andrade & António Portugal Duarte, 2014. "Output-gaps in the PIIGS Economies: An Ingredient of a Greek Tragedy," GEMF Working Papers 2014-06, GEMF, Faculty of Economics, University of Coimbra.
    6. Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "Inflation and monetary policy in the twentieth century," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 27(Q I), pages 22-45.
    7. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
    8. King, Robert G. & Rebelo, Sergio T., 1999. "Resuscitating real business cycles," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 14, pages 927-1007, Elsevier.
    9. Celsa Machado, 2001. "Measuring Business Cycles: The Real Business Cycle Approach and Related Controversies," FEP Working Papers 107, Universidade do Porto, Faculdade de Economia do Porto.
    10. 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.
    11. L.J. Christiano & C.J. Gust, 1999. "Taylor Rules in a Limited Participation Model," DNB Staff Reports (discontinued) 33, Netherlands Central Bank.
    12. Ince, Onur & Papell, David H., 2013. "The (un)reliability of real-time output gap estimates with revised data," Economic Modelling, Elsevier, vol. 33(C), pages 713-721.
    13. Timothy Cogley & Thomas J. Sargent, 2005. "The conquest of US inflation: Learning and robustness to model uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 528-563, April.
    14. Richard Ashley & Randal Verbrugge, 2009. "Frequency Dependence in Regression Model Coefficients: An Alternative Approach for Modeling Nonlinear Dynamic Relationships in Time Series," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 4-20.
    15. den Haan, Wouter J. & Sumner, Steven W., 2004. "The comovement between real activity and prices in the G7," European Economic Review, Elsevier, vol. 48(6), pages 1333-1347, December.
    16. Siu, Henry E., 2008. "Time consistent monetary policy with endogenous price rigidity," Journal of Economic Theory, Elsevier, vol. 138(1), pages 184-210, January.
    17. Srinivasan, Naveen & Jain, Sumit & Ramachandran, M., 2009. "Monetary policy and the behaviour of inflation in India: Is there a need for institutional reform?," Journal of Asian Economics, Elsevier, vol. 20(1), pages 13-24, January.
    18. Hayat, Zafar & Balli, Faruk & Obben, James & Shakur, Shamim, 2016. "An empirical assessment of monetary discretion: The case of Pakistan," Journal of Policy Modeling, Elsevier, vol. 38(5), pages 954-970.
    19. Leduc, Sylvain & Sill, Keith & Stark, Tom, 2007. "Self-fulfilling expectations and the inflation of the 1970s: Evidence from the Livingston Survey," Journal of Monetary Economics, Elsevier, vol. 54(2), pages 433-459, March.
    20. Richard A. Ashley. & Randall J. Verbrugge., 2006. "Mis-Specification and Frequency Dependence in a New Keynesian Phillips Curve," Working Papers e06-12, Virginia Polytechnic Institute and State University, Department of Economics.

    More about this item

    Keywords

    Time-series analysis;

    JEL classification:

    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    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:fip:fedcwp:9906. 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: . General contact details of provider: https://edirc.repec.org/data/frbclus.html .

    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: (email available below). General contact details of provider: https://edirc.repec.org/data/frbclus.html .

    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.