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A Multivariate Band-Pass Filter

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  • João Valle e Azevedo

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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Bibliographic Info

Paper provided by Banco de Portugal, Economics and Research Department in its series Working Papers with number w200717.

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Date of creation: 2007
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Handle: RePEc:ptu:wpaper:w200717

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References

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  1. Athanasios Orphanides & Simon van Norden, 1999. "The reliability of output gap estimates in real time," Finance and Economics Discussion Series 1999-38, Board of Governors of the Federal Reserve System (U.S.).
  2. Harvey,Andrew C., 1990. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521321969, October.
  3. 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.
  4. James H. Stock & Mark W. Watson, 1998. "Business Cycle Fluctuations in U.S. Macroeconomic Time Series," NBER Working Papers 6528, National Bureau of Economic Research, Inc.
  5. Pierce, David A., 1980. "Data revisions with moving average seasonal adjustment procedures," Journal of Econometrics, Elsevier, vol. 14(1), pages 95-114, September.
  6. 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.
  7. Lawrence J. Christiano & Terry J. Fitzgerald, 1999. "The Band pass filter," Working Paper 9906, Federal Reserve Bank of Cleveland.
    • 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.
  8. Gerhard Runstler, 2004. "Modelling phase shifts among stochastic cycles," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 232-248, 06.
  9. Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
  10. 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.
  11. repec:fth:baesse:9912 is not listed on IDEAS
  12. 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.
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Cited by:
  1. 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.
  2. Ana Sequeira, 2013. "Predicting aggregate returns using valuation ratios out-of-sample," Economic Bulletin and Financial Stability Report Articles, Banco de Portugal, Economics and Research Department.
  3. 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.
  4. Drew Creal & Siem Jan Koopman & Eric Zivot, 2008. "Extracting a Robust U.S. Business Cycle Using a Time-Varying Multivariate Model-Based Bandpass Filter," Working Papers UWEC-2008-15-FC, University of Washington, Department of Economics.
  5. repec:dgr:uvatin:2008069 is not listed on IDEAS
  6. João Valle e Azevedo & Ana Pereira, 2013. "Macroeconomic Forecasting Using Low-Frequency Filters," Working Papers w201301, Banco de Portugal, Economics and Research Department.

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