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

Michel Fliess (1, 2) , Cédric Join (3, 4, 2)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 ALIEN
3 Inria Lille - Nord Europe
4 CRAN - Centre de Recherche en Automatique de Nancy

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.

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

Domains: Statistical Finance [q-fin.ST]; Computational Finance [q-fin.CP]; Computational Engineering, Finance, and Science [cs.CE]; Data Structures and Algorithms [cs.DS]; Other Statistics [stat.ML]; Logic [math.LO]

Michel Fliess, Cédric Join. Seasonalities and cycles in time series: A fresh look with computer experiments. Paris Financial Management Conference, PFMC 2015, Dec 2015, Paris, France. ⟨hal-01208171⟩