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

Author

Listed:
  • Siem Jan Koopman

    (Vrije Universiteit Amsterdam)

  • Soon Yip Wong

    (Vrije Universiteit Amsterdam)

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.

Suggested Citation

  • Siem Jan Koopman & Soon Yip Wong, 2006. "Extracting Business Cycles using Semi-parametric Time-varying Spectra with Applications to US Macroeconomic Time Series," Tinbergen Institute Discussion Papers 06-105/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20060105
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    File URL: https://papers.tinbergen.nl/06105.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Frequency domain estimation; frequency domain bootstrap; time-varying parameters; unobserved components models;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single 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

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