A Multivariate Band-Pass Filter
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.
|Date of creation:||2007|
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- Lawrence J. Christiano & Terry J. Fitzgerald, 1999.
"The Band pass filter,"
9906, Federal Reserve Bank of Cleveland.
- 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.
- Athanasios Orphanides & Simon van Norden, 1999.
"The Reliability of Output Gap Estimates in Real Time,"
- 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, 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.
- 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.).
- 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
- 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.
- Pierce, David A., 1980. "Data revisions with moving average seasonal adjustment procedures," Journal of Econometrics, Elsevier, vol. 14(1), pages 95-114, September.
- 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:cup:cbooks:9780521321969 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.
- Velasco, Carlos, 1999. "Non-stationary log-periodogram regression," Journal of Econometrics, Elsevier, vol. 91(2), pages 325-371, August.
- Regina Kaiser & Agustín Maravall, 1999.
"Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter,"
Banco de Espa�a Working Papers
9912, Banco de Espa�a.
- 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.
- Gerhard Runstler, 2004. "Modelling phase shifts among stochastic cycles," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 232-248, 06.
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