A Multivariate Band-Pass Filter
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Banco de Portugal, Economics and Research Department in its series Working Papers with number w200717.
Date of creation: 2007
Date of revision:
Other versions of this item:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
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.:
- 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.).
- 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.
- Athanasios Orphanides & Simon van Norden, 1999. "The Reliability of Output Gap Estimates in Real Time," Macroeconomics 9907006, EconWPA.
- Athanasios Orphanides & Simon van Norden, 2001. "The Unreliability of Output Gap Estimates in Real Time," CIRANO Working Papers 2001s-57, CIRANO.
- Athanasios Orphanides & Simon Van_Norden, 2000. "The Reliability of Output Gap Estimates in Real Time," Econometric Society World Congress 2000 Contributed Papers 0768, Econometric Society.
- Harvey,Andrew C., 1990.
"Forecasting, Structural Time Series Models and the Kalman Filter,"
Cambridge University Press, number 9780521321969, October.
- Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, October.
- 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.
- 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.
- 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.
- Pierce, David A., 1980. "Data revisions with moving average seasonal adjustment procedures," Journal of Econometrics, Elsevier, vol. 14(1), pages 95-114, September.
- 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.
- Regina Kaiser & Agustín Maravall, 1999. "Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter," Banco de Espaï¿½a Working Papers 9912, Banco de Espa�a.
- Lawrence J. Christiano & Terry J. Fitzgerald, 1999.
"The Band pass filter,"
9906, Federal Reserve Bank of Cleveland.
- Gerhard Runstler, 2004. "Modelling phase shifts among stochastic cycles," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 232-248, 06.
- Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
- 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.
- repec:fth:baesse:9912 is not listed on IDEAS
- 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.
- 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.
- 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.
- 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.
- Drew Creal & Siem Jan Koopman & Eric Zivot, 2008.
"Extracting a Robust U.S. Business Cycle Using a Time-Varying Multivariate Model-Based Bandpass Filter,"
UWEC-2008-15-FC, University of Washington, Department of Economics.
- Drew Creal & Siem Jan Koopman & Eric Zivot, 2010. "Extracting a robust US business cycle using a time-varying multivariate model-based bandpass filter," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 695-719.
- repec:dgr:uvatin:2008069 is not listed on IDEAS
- João Valle e Azevedo & Ana Pereira, 2013. "Macroeconomic Forecasting Using Low-Frequency Filters," Working Papers w201301, Banco de Portugal, Economics and Research Department.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (DEE-NTDD).
If references are entirely missing, you can add them using this form.