Identifying economic periods and crisis with the multidimensional scaling

J. Tenreiro Machado (1) , Gonçalo Monteiro Duarte (2) , Fernando B. Duarte (3)

1 Department of Electrical Engineering
2 Universidade Lusófona de Humanidades e Tecnologias [Lisbon]
3 Department of Mathematics

This paper applied MDS and Fourier transform to analyze different periods of the business cycle. With such purpose, four important stock market indexes (Dow Jones, Nasdaq, NYSE, S&P500) were studied over time. The analysis under the lens of the Fourier transform showed that the indexes have characteristics similar to those of fractional noise. By the other side, the analysis under the MDS lens identified patterns in the stock markets specific to each economic expansion period. Although the identification of patterns characteristic to each expansion period is interesting to practitioners (even if only in a posteriori fashion), further research should explore the meaning of such regularities and target to find a method to estimate future crisis.

Mots clés: Multidimensional scaling; Fractional calculus; Fourier transform; Economic cycle

J. Tenreiro Machado, Gonçalo Monteiro Duarte, Fernando B. Duarte. Identifying economic periods and crisis with the multidimensional scaling. Nonlinear Dynamics, 2010, 63 (4), pp.611-622. ⟨10.1007/s11071-010-9823-2⟩. ⟨hal-00620891⟩