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Time-spectral density and wavelets approaches. Comparative study. Applications to SP500 returns and US GDP

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  • Ahamada, Ibrahim
  • Jolivaldt, Philippe
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    Abstract

    Various forms of instability can be observed in macroeconomic and financial data including changes in variance, changes in cycle properties, or both. Traditional tests do not allow to distinguish between these different cases. This paper proposes and compares two alternative approaches. The comparison is based on Monte Carlo simulations. The first approach is based on windowed-estimate of the time-spectral density, while the second method is the wavelets theory. We show that the wavelets approach is particularly powerful to detect changes in cyclical properties, while the first approach fails in such a case. In contrast, the wavelets method fails to capture time–interaction effects, while the first approach is more powerful regarding this point. Hence the two methods are complementary. A first application on the SP500 returns shows that there are only changes in variance without altering the cyclical properties of the series. A second application on the US growth rate allows to conclude that there are simultaneous changes in the time and frequency domain.

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    Bibliographic Info

    Article provided by Elsevier in its journal Economic Modelling.

    Volume (Year): 31 (2013)
    Issue (Month): C ()
    Pages: 460-466

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    Handle: RePEc:eee:ecmode:v:31:y:2013:i:c:p:460-466

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    Web page: http://www.elsevier.com/locate/inca/30411

    Related research

    Keywords: Time–frequency domain; Time-spectral density; Wavelets; Covariance-stationarity; Monte Carlo simulation;

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    1. Crowley, Patrick, 2005. "An intuitive guide to wavelets for economists," Research Discussion Papers 1/2005, Bank of Finland.
    2. BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche 9807, Universite de Montreal, Departement de sciences economiques.
    3. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
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