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Extracting Business Cycles using Semi-parametric Time-varying Spectra with Applications to US Macroeconomic Time Series

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Author Info
Siem Jan Koopman () (Vrije Universiteit Amsterdam)
Soon Yip Wong () (Vrije Universiteit Amsterdam)

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Abstract

A growing number of empirical studies provides evidence that dynamic properties of macroeconomic time series have been changing over time. Model-based procedures for the measurement of business cycles should therefore allow model parameters to adapt over time. In this paper the time dependencies of parameters are implied by a time dependent sample spectrum. Explicit model specifications for the parameters are therefore not required. Parameter estimation is carried out in the frequency domain by maximising the spectral likelihood function. The time dependent spectrum is specified as a semi-parametric smoothing spline ANOVA function that can be formulated in state space form. Since the resulting spectral likelihood function is time-varying, model parameter estimates become time-varying as well. This new and simple approach to business cycle extraction includes bootstrap procedures for the computation of confidence intervals and real-time procedures for the forecasting of the spectrum and the business cycle. We illustrate the methodology by presenting a complete business cycle analysis for two U.S. macroeconomic time series. The empirical results are promising and provide significant evidence for the great moderation of the U.S. business cycle.

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Publisher Info
Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 06-105/4.

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Date of creation: 29 Nov 2006
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Handle: RePEc:dgr:uvatin:20060105

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Web page: http://www.tinbergen.nl/

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Related research
Keywords: Frequency domain estimation; frequency domain bootstrap; time-varying parameters; unobserved components models;

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
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
E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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    Other versions:
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  3. Rob Luginbuhl & Siem Jan Koopman, 2004. "Convergence in European GDP series: a multivariate common converging trend-cycle decomposition," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(5), pages 611-636. [Downloadable!]
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    Other versions:
  6. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept. [Downloadable!] (restricted)
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    Other versions:
  15. Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, 03. [Downloadable!] (restricted)
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  16. Rob Luginbuhl & Siem Jan Koopman, 2003. "Convergence in European GDP Series," Tinbergen Institute Discussion Papers 03-031/4, Tinbergen Institute. [Downloadable!]
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