Nonlinear Dynamics and Wavelets for Business Cycle Analysis

  • Peter Martey Addo
  • Monica Billio
  • Dominique Guégan
Part of the Dynamic Modeling and Econometrics in Economics and Finance book series (DMEF, volume 20)


We provide a signal modality analysis to characterize and detect nonlinearity schemes in the US Industrial Production Index time series. The analysis is achieved by using the recently proposed “delay vector variance” (DVV) method, which examines local predictability of a signal in the phase space to detect the presence of determinism and nonlinearity in a time series. Optimal embedding parameters used in the DVV analysis are obtained via a differential entropy based method using Fourier and wavelet-based surrogates. A complex Morlet wavelet is employed to detect and characterize the US business cycle. A comprehensive analysis of the feasibility of this approach is provided. Our results coincide with the business cycles peaks and troughs dates published by the National Bureau of Economic Research (NBER).



The authors are grateful to the Editors and anonymous referees for their careful revision, valuable suggestions, and comments that have improved this paper. We thank the conference participants of ISCEF 2012, CFE–ERCIM 2012, COMPSTAT 2012 and the participants at the Econometrics Internal Seminar at Center for Operations Research and Econometrics (CORE) for their participation and interest. We also would like to thank Sébastien Van Bellegem, Luc Bauwens, Christian Hafner, Timo Terasvirta and Yukai Kevin Yang for their remarks and questions. In this paper, we made use of the algorithms in wavelet toolbox in Matlab and DVV toolbox available from mandic/dvv.htm. The wavelet-based (wiAAFT) surrogates algorithm used in this paper may be downloaded from The first author acknowledges financial support under Erasmus Mundus fellowship.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Peter Martey Addo
    • 1
    • 2
    • 3
  • Monica Billio
    • 2
  • Dominique Guégan
    • 4
  1. 1.European Doctorate in Economics–Erasmus Mundus (EDEEM)Université Paris 1 - Panthéon-SorbonneParisFrance
  2. 2.Department of EconomicsUniversità Ca’Foscari of VeniceVeniceItaly
  3. 3.Université Paris 1- Panthéon-SorbonneParisFrance
  4. 4.Université Paris I—Panthéon SorbonneParisFrance

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