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

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  • 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.

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Bibliographic 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

Related research

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

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  2. Chang-Jin Kim & Charles Nelson & Jeremy M. Piger, 2003. "The less volatile U.S. economy: a Bayesian investigation of timing, breadth, and potential explanations," Working Papers, Federal Reserve Bank of St. Louis 2001-016, Federal Reserve Bank of St. Louis.
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  8. van Dijk, Dick & Teräsvirta, Timo & Franses, Philip Hans, 2000. "Smooth Transition Autoregressive Models - A Survey of Recent Developments," Working Paper Series in Economics and Finance 380, Stockholm School of Economics, revised 17 Jan 2001.
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