Un método topológico para el análisis de complejidad de series de tiempo

Erika Rodriguez; Benjamín A  Itzá-Ortiz; Federico  Menéndez-Conde Lara; Margarita  Tetlalmatzi-Montiel; Rafael Villarroel-Flores

doi:10.29057/icbi.v9i17.7137

Erika Rodriguez Universidad Autónoma del Estado de Hidalgo https://orcid.org/0000-0002-7738-1863
Benjamín A Itzá-Ortiz Universidad Autónoma del Estado de Hidalgo https://orcid.org/0000-0002-6189-3266
Federico Menéndez-Conde Lara Universidad Autónoma del Estado de Hidalgo https://orcid.org/0000-0002-8741-4331
Margarita Tetlalmatzi-Montiel Universidad Autónoma del Estado de Hidalgo https://orcid.org/0000-0003-3659-1538
Rafael Villarroel-Flores Universidad Autónoma del Estado de Hidalgo https://orcid.org/0000-0003-4295-5414

DOI: https://doi.org/10.29057/icbi.v9i17.7137

Keywords: Time series, topology,, homology, networks, simplicial complexes.

Abstract

In this article, a method based on algebraic topology for the analysis of vector valued time series is proposed. Each time series corresponds to a variable. The correlation matrix for these variables is constructed and the corresponding weighted network is considered. A filtration of simplicial complexes is then obtained by the variation of a parameter p between 0 and 1. The analysis on the number of cavities of the simplicial complex is conducted by means of studding the variation of the Betti numbers of the complexes in the filtration. By means of computer simulations, we get results suggesting that in case the correlation matrix is induced by vector valued time series modeling natural phenomena, the complexity on the variations of the Betti numbers is significantly lower than for random correlation matrices.

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Author Biographies

Erika Rodriguez, Universidad Autónoma del Estado de Hidalgo

PhD in Neuroscience, CINVESTAV del IPN, 2013.

Masters in Neuroscience, University of Oregon, Eugene, EEUU, 2003.

Bachelor's degree in Computer Science. Autonomous University of Yucatán, Mérida, Mexico, June 1998.

Benjamín A Itzá-Ortiz, Universidad Autónoma del Estado de Hidalgo

PhD in mathematics, University of Oregon, Eugene, EEUU, 2003.
Master in mathematics , Tulane University, New Orleans, EEUU, 1997.
Bachelor's degree in mathematics, Universidad Autónoma de Yucatán, Mérida, México, 1995.

Federico Menéndez-Conde Lara, Universidad Autónoma del Estado de Hidalgo

PhD in Mathematics, Centre for Mathematical Análisis and its Applications (CMAIA), University of Sussex, Brighton , Inglaterra, 2002.
- Master´s in mathematics, Centro de Investigación en Matemáticas (CIMAT), Guanajuato, México. 1997.
- Bachelor´s degree in Mathematics, Universidad de las Américas - Puebla, 1996.

Margarita Tetlalmatzi-Montiel, Universidad Autónoma del Estado de Hidalgo

Master´s in mathematics, University of Virginia, U.S.A., 1989.
Bachelor of Physics and Mathematics, Escuela Superior de Física y Matemáticas, IPN, 1993.

Rafael Villarroel-Flores, Universidad Autónoma del Estado de Hidalgo

PhD in mathematics, School of Mathematics, University of Minnesota, 1996.
Master's in mathematics, Facultad de Ciencias, UNAM, 1993.
Bachelor's degree in mathematics, Facultad de Ciencias, UNAM, 1991.

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