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Stochastic trends and seasonality in economic time series: new evidence from Bayesian stochastic model specification search

  • Stefano Grassi

    ()

    (Aarhus University and CREATES)

  • Tommaso Proietti

    ()

    (University of Sydney)

An important issue in modelling economic time series is whether key unobserved components representing trends, seasonality and calendar components, are deterministic or evolutive. We address it by applying a recently proposed Bayesian variable selection methodology to an encompassing linear mixed model that features, along with deterministic effects, additional random explanatory variables that account for the evolution of the underlying level, slope, seasonality and trading days. Variable selection is performed by estimating the posterior model probabilities using a suitable Gibbs sampling scheme. The paper conducts an extensive empirical application on a large and representative set of monthly time series concerning industrial production and retail turnover. We find strong support for the presence of stochastic trends in the series, either in the form of a time-varying level, or, less frequently, of a stochastic slope, or both. Seasonality is a more stable component: only in 70% of the cases we were able to select at least one stochastic trigonometric cycle out of the six possible cycles. Most frequently the time variation is found in correspondence with the fundamental and the first harmonic cycles. An interesting and intuitively plausible finding is that the probability of estimating time-varying components increases with the sample size available. However, even for very large sample sizes we were unable to find stochastically varying calendar effects.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2011-30.

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Length: 24
Date of creation: 02 Sep 2011
Date of revision:
Handle: RePEc:aah:create:2011-30
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Koop, Gary & Dijk, Herman K. Van, 2000. "Testing for integration using evolving trend and seasonals models: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 97(2), pages 261-291, August.
  2. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2010. "Stochastic model specification search for Gaussian and partial non-Gaussian state space models," Journal of Econometrics, Elsevier, vol. 154(1), pages 85-100, January.
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  9. Stefano Grassi & Tommaso Proietti, 2011. "Bayesian stochastic model specification search for seasonal and calendar effects," CREATES Research Papers 2011-08, School of Economics and Management, University of Aarhus.
  10. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
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  14. Koop, Gary, 1992. "'Objective' Bayesian Unit Root Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(1), pages 65-82, Jan.-Marc.
  15. Grassi, S. & Proietti, T., 2014. "Characterising economic trends by Bayesian stochastic model specification search," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 359-374.
  16. Hylleberg, S. (ed.), 1992. "Modelling Seasonality," OUP Catalogue, Oxford University Press, number 9780198773184.
  17. Christopher A. Sims, 1988. "Bayesian skepticism on unit root econometrics," Discussion Paper / Institute for Empirical Macroeconomics 3, Federal Reserve Bank of Minneapolis.
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