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Seasonalities and cycles in time series: A fresh look with computer experiments

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  • Michel Fliess

    (LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, ALIEN)

  • Cédric Join

    (Inria Lille - Nord Europe - Inria - Institut National de Recherche en Informatique et en Automatique, CRAN - Centre de Recherche en Automatique de Nancy - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique, ALIEN)

Abstract

Recent advances in the understanding of time series permit to clarify seasonalities and cycles, which might be rather obscure in today's literature. A theorem due to P. Cartier and Y. Perrin, which was published only recently, in 1995, and several time scales yield, perhaps for the first time, a clear-cut definition of seasonalities and cycles. Their detection and their extraction, moreover, become easy to implement. Several computer experiments with concrete data from various fields are presented and discussed. The conclusion suggests the application of this approach to the debatable Kondriatev waves.

Suggested Citation

  • Michel Fliess & Cédric Join, 2015. "Seasonalities and cycles in time series: A fresh look with computer experiments," Post-Print hal-01208171, HAL.
    • Handle: RePEc:hal:journl:hal-01208171
    Note: View the original document on HAL open archive server: https://polytechnique.hal.science/hal-01208171
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    References listed on IDEAS

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    1. Svetlana Borovkova & Helyette Geman, 2006. "Seasonal and stochastic effects in commodity forward curves," Review of Derivatives Research, Springer, vol. 9(2), pages 167-186, September.
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    More about this item

    Keywords

    detection; decomposition; cycles; seasonalities; time series; time scales; nonstandard analysis; deseasonalization; Kondriatev waves; extraction; trend;
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