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A Multivariate Band-Pass Filter

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Author Info
Valle e Azevedo, João

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Abstract

We develop a multivariate filter which is an optimal (in the mean squared error sense) approximation to the ideal filter that isolates a specified range of fluctuations in a time series, e.g., business cycle fluctuations in macroeconomic time series. This requires knowledge of the true second-order moments of the data. Otherwise these can be estimated and we show empirically that the method still leads to relevant improvements of the extracted signal, especially in the endpoints of the sample. Our filter is an extension of the univariate filter developed by Christiano and Fitzgerald (2003). Specifically, we allow an arbitrary number of covariates to be employed in the estimation of the signal. We illustrate the application of the filter by constructing a business cycle indicator for the U.S. economy. The filter can additionally be used in any similar signal extraction problem demanding accurate real-time estimates.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 6555.

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Date of creation: 02 Jan 2008
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Handle: RePEc:pra:mprapa:6555

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Find related papers by JEL classification:
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
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  2. Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Paper 9906, Federal Reserve Bank of Cleveland. [Downloadable!]
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    • Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band Pass Filter," NBER Working Papers 7257, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    • 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, 05. [Downloadable!] (restricted)
  3. Pierce, David A., 1980. "Data revisions with moving average seasonal adjustment procedures," Journal of Econometrics, Elsevier, vol. 14(1), pages 95-114, September. [Downloadable!] (restricted)
  4. Gomez, Victor, 2001. "The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 365-73, July.
  5. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter," Banco de España Working Papers 9912, Banco de España.
  6. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
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  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, 07. [Downloadable!] (restricted)
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  9. Valle e Azevedo, Joao & Koopman, Siem Jan & Rua, Antonio, 2006. "Tracking the Business Cycle of the Euro Area: A Multivariate Model-Based Bandpass Filter," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 278-290, July. [Downloadable!] (restricted)
  10. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter," Banco de España Working Papers 9912, Banco de España.
  11. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the business cycle: A modified Hodrick-Prescott filter," Spanish Economic Review, Springer, vol. 1(2), pages 175-206. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Drew Creal & Siem Jan Koopman & Eric Zivot, 2008. "The Effect of the Great Moderation on the U.S. Business Cycle in a Time-varying Multivariate Trend-cycle Model," Tinbergen Institute Discussion Papers 08-069/4, Tinbergen Institute. [Downloadable!]
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  2. Mark W. Watson, 2007. "How accurate are real-time estimates of output trends and gaps?," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 143-161. [Downloadable!]
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